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Energy Transfer

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Thermodynamic Limits Around M-dwarf Stars: Acknowledgements

(1) Samir Chitnavis, School of Biological and Behavioural Sciences, Queen Mary University of London, Mile End, London E1 4NS, UK & Digital Environment Research Institute, Queen Mary University of London, Empire House, Whitechapel E1 1HH, UK;
(2) Thomas J. Haworth, Astronomy Unit, Queen Mary University of London, Mile End Road, London E1 4NS, UK;
(3) Edward Gillen, Astronomy Unit, Queen Mary University of London, Mile End Road, London E1 4NS, UK;
(4) Conrad W. Mullineaux, School of Biological and Behavioural Sciences, Queen Mary University of London, Mile End, London E1 4NS, UK;
(5) Christopher D. P. Duffy, School of Biological and Behavioural Sciences, Queen Mary University of London, Mile End, London E1 4NS, UK & Digital Environment Research Institute, Queen Mary University of London, Empire House, Whitechapel E1 1HH, UK (Email: c.duffy@qmul.ac.uk). Table of Links Abstract and Introduction
2 Methodology
2.1 Local spectral irradiance as a function of stellar temperature
2.2 Thermodynamic model of an oxygenic light-harvesting system
2.3 Lattice model of an oxygenic light-harvesting system
3 Results
3.1 Orbital distances and incident spectral fluxes
3.2 Thermodynamic antenna model: Increasing antenna size in limited PAR
3.3 Lattice antenna model: Increasing the size of a “flat” antenna in limited PAR
3.4 Lattice antenna model: Improving antenna efficiency with an energetic ’funnel’
4 Discussion
Acknowledgements, Author Contribution Statement, Authors disclosure statement and References 4 Discussion The results of our generalized antenna models suggest that the oxygenic photosynthesis is likely feasible on exo-planets orbiting low mass M-dwarf stars, though there are some restrictions. A light-harvesting system similar to PSII of vascular plants (but with a larger antenna) would be severely entropy-limited even before we factor in local limitations like water scarcity, atmospheric attenuation of light, etc. However, this reflects the fact that plants are evolved to deal with highly variable irradiance [Vialet-Chabrand et al., 2017, Li et al., 2021] rather than constant low light. One of the major risks to plants is actually excessive illumination which can cause oxidative damage to PSII, a metabolically costly phenomenon known as photoinhibition, and one that should be familiar to anyone who has suddenly moved a houseplant into full sun. To mitigate photoinhibition [Aro et al., 1993], plants possess regulatory mechanisms that suppress photon absorption and down-regulate the antenna [Ruban, 2016, Ruban and Wilson, 2021]. Therefore it is unsurprising that such a system does not perform well in severely PAR-depleted light. However, by introducing an energetic gradient to the antenna (the energy funnel) we were able to significantly improve antenna efficiency and electron output. Of the branched and hexagonal antenna topologies the former performs better, able to match the performance of the latter but with fewer LHC subunits and a shallower energetic gradient. Fewer LHC subunits is perhaps the most important factor as it is directly related to the metabolic “cost” of the antenna. Of course, there are countless other modifications that could be made to the antenna. For example, one could increase pigment density which would increase the overall cross-section of each LHC and enhance inter-pigment energy transfer. The pigment concentration in LHCII is already very high, approximately 1 mol dm−3 , and the protein scaffold enforces highly specific inter-pigment distances and relative orientations to avoid dissipative processes such as concentration quenching [Liu et al., 2004]. However, one could imagine an adaptation similar to the chlorosome antenna of green sulphur bacteria [Oostergetel et al., 2010]. This structure is a solid aggregate of ∼ 300, 000 BChls encapsulated in a membrane sheath, effectively the densest pigment packing possible, and it facilitates (anoxygenic) photosynthesis in extremely low illumination. It should be noted however that such as structure is is a significant metabolic investment and one that is not seen in any large multi-cellular organism. Alternatively, one could replace Chl a and b with pigments with larger intrinsic cross-sections and/or absorption widths, which would increase the rate of photon absorption, γi . Since intermolecular energy transfer depends on the oscillator strengths and spectral overlap of the pigments involved, this may also enhance the intrinsic transfer rates, (Ki,j ) −1 . Still, the branched, funnel antenna strategy is a plausible one because it explicitly addresses the fundamental thermodynamic limits inherent in light-harvesting. More importantly, such an antenna actually exists on in Earth in the form of the phycobilisome of oxygenic cyanobacteria [Saer and Blankenship, 2017]. Like our model, the phycobilisome is modular and can adapt to changes in irradiance. Kolodny et al. [2022] recently showed that cyanobacteria in deep water, where light is very blue-shifted, will lenghten their phycobilisome rods by adding more terminal PE subunits and will increase overall antenna efficiency, ϕF , by tuning pigment content (and possibly density). The most important result, however, is the recent work of Battistuzzi et al. [2023] who showed that cyanobacteria could comfortably adapt to the the light typical of M-dwarf stars. Moreover, they used a sophisticated starlight simulator setup which models atmospheric attenuation of light, meaning their cyanobacteria were likely subject to ever scanter illumination than we consider here. Interestingly, they also considered pure “far red” (700−800 nm) illumination and found that this retarded growth rate relative to the M-dwarf light, implying that, as in our model, the organism was adapting its antenna to intercept more photons in the depleted PAR region.It should be noted that they also considered on the red-adapted strains described in the introduction that fared equally well in M-dwarf and far red light. Strictly, both our modelling and the experimental work of Kolodny et al. [2022]. concerns the acclimation of an existing antenna to an unusual lightenvironment rather than the ground-up evolution of an antenna structure specifically optimized to it. Nevertheless, Kolodny’s work demonstrates that oxygenic photosynthesis is, in principle, possible around very low mass stars and our findings indicate that the key consideration is overcoming a fundamental entropic barrier to light-harvesting. This paper is available on arxiv under CC 4.0 license. (1) Samir Chitnavis, School of Biological and Behavioural Sciences, Queen Mary University of London, Mile End, London E1 4NS, UK & Digital Environment Research Institute, Queen Mary University of London, Empire House, Whitechapel E1 1HH, UK; (2) Thomas J. Haworth, Astronomy Unit, Queen Mary University of London, Mile End Road, London E1 4NS, UK; (3) Edward Gillen, Astronomy Unit, Queen Mary University of London, Mile End Road, London E1 4NS, UK; (4) Conrad W. Mullineaux, School of Biological and Behavioural Sciences, Queen Mary University of London, Mile End, London E1 4NS, UK; (5) Christopher D. P. Duffy, School of Biological and Behavioural Sciences, Queen Mary University of London, Mile End, London E1 4NS, UK & Digital Environment Research Institute, Queen Mary University of London, Empire House, Whitechapel E1 1HH, UK (Email: c.duffy@qmul.ac.uk). (1) Samir Chitnavis, School of Biological and Behavioural Sciences, Queen Mary University of London, Mile End, London E1 4NS, UK & Digital Environment Research Institute, Queen Mary University of London, Empire House, Whitechapel E1 1HH, UK; (2) Thomas J. Haworth, Astronomy Unit, Queen Mary University of London, Mile End Road, London E1 4NS, UK; (3) Edward Gillen, Astronomy Unit, Queen Mary University of London, Mile End Road, London E1 4NS, UK; (4) Conrad W. Mullineaux, School of Biological and Behavioural Sciences, Queen Mary University of London, Mile End, London E1 4NS, UK; (5) Christopher D. P. Duffy, School of Biological and Behavioural Sciences, Queen Mary University of London, Mile End, London E1 4NS, UK & Digital Environment Research Institute, Queen Mary University of London, Empire House, Whitechapel E1 1HH, UK (Email: c.duffy@qmul.ac.uk). Table of Links Abstract and Introduction 2 Methodology 2.1 Local spectral irradiance as a function of stellar temperature 2.2 Thermodynamic model of an oxygenic light-harvesting system 2.3 Lattice model of an oxygenic light-harvesting system 3 Results 3.1 Orbital distances and incident spectral fluxes 3.2 Thermodynamic antenna model: Increasing antenna size in limited PAR 3.3 Lattice antenna model: Increasing the size of a “flat” antenna in limited PAR 3.4 Lattice antenna model: Improving antenna efficiency with an energetic ’funnel’ 4 Discussion Acknowledgements, Author Contribution Statement, Authors disclosure statement and References Abstract and Introduction Abstract and Introduction 2 Methodology 2.1 Local spectral irradiance as a function of stellar temperature 2.1 Local spectral irradiance as a function of stellar temperature 2.2 Thermodynamic model of an oxygenic light-harvesting system 2.2 Thermodynamic model of an oxygenic light-harvesting system 2.3 Lattice model of an oxygenic light-harvesting system 2.3 Lattice model of an oxygenic light-harvesting system 3 Results 3.1 Orbital distances and incident spectral fluxes 3.1 Orbital distances and incident spectral fluxes 3.2 Thermodynamic antenna model: Increasing antenna size in limited PAR 3.2 Thermodynamic antenna model: Increasing antenna size in limited PAR 3.3 Lattice antenna model: Increasing the size of a “flat” antenna in limited PAR 3.3 Lattice antenna model: Increasing the size of a “flat” antenna in limited PAR 3.4 Lattice antenna model: Improving antenna efficiency with an energetic ’funnel’ 3.4 Lattice antenna model: Improving antenna efficiency with an energetic ’funnel’ 4 Discussion 4 Discussion Acknowledgements, Author Contribution Statement, Authors disclosure statement and References Acknowledgements, Author Contribution Statement, Authors disclosure statement and References 4 Discussion The results of our generalized antenna models suggest that the oxygenic photosynthesis is likely feasible on exo-planets orbiting low mass M-dwarf stars, though there are some restrictions. A light-harvesting system similar to PSII of vascular plants (but with a larger antenna) would be severely entropy-limited even before we factor in local limitations like water scarcity, atmospheric attenuation of light, etc. However, this reflects the fact that plants are evolved to deal with highly variable irradiance [Vialet-Chabrand et al., 2017, Li et al., 2021] rather than constant low light. One of the major risks to plants is actually excessive illumination which can cause oxidative damage to PSII, a metabolically costly phenomenon known as photoinhibition, and one that should be familiar to anyone who has suddenly moved a houseplant into full sun. To mitigate photoinhibition [Aro et al., 1993], plants possess regulatory mechanisms that suppress photon absorption and down-regulate the antenna [Ruban, 2016, Ruban and Wilson, 2021]. Therefore it is unsurprising that such a system does not perform well in severely PAR-depleted light. However, by introducing an energetic gradient to the antenna (the energy funnel) we were able to significantly improve antenna efficiency and electron output. Of the branched and hexagonal antenna topologies the former performs better, able to match the performance of the latter but with fewer LHC subunits and a shallower energetic gradient. Fewer LHC subunits is perhaps the most important factor as it is directly related to the metabolic “cost” of the antenna. Of course, there are countless other modifications that could be made to the antenna. For example, one could increase pigment density which would increase the overall cross-section of each LHC and enhance inter-pigment energy transfer. The pigment concentration in LHCII is already very high, approximately 1 mol dm−3 , and the protein scaffold enforces highly specific inter-pigment distances and relative orientations to avoid dissipative processes such as concentration quenching [Liu et al., 2004]. However, one could imagine an adaptation similar to the chlorosome antenna of green sulphur bacteria [Oostergetel et al., 2010]. This structure is a solid aggregate of ∼ 300, 000 BChls encapsulated in a membrane sheath, effectively the densest pigment packing possible, and it facilitates (anoxygenic) photosynthesis in extremely low illumination. It should be noted however that such as structure is is a significant metabolic investment and one that is not seen in any large multi-cellular organism. Alternatively, one could replace Chl a and b with pigments with larger intrinsic cross-sections and/or absorption widths, which would increase the rate of photon absorption, γi . Since intermolecular energy transfer depends on the oscillator strengths and spectral overlap of the pigments involved, this may also enhance the intrinsic transfer rates, (Ki,j ) −1 . Still, the branched, funnel antenna strategy is a plausible one because it explicitly addresses the fundamental thermodynamic limits inherent in light-harvesting. More importantly, such an antenna actually exists on in Earth in the form of the phycobilisome of oxygenic cyanobacteria [Saer and Blankenship, 2017]. Like our model, the phycobilisome is modular and can adapt to changes in irradiance. Kolodny et al. [2022] recently showed that cyanobacteria in deep water, where light is very blue-shifted, will lenghten their phycobilisome rods by adding more terminal PE subunits and will increase overall antenna efficiency, ϕF , by tuning pigment content (and possibly density). The most important result, however, is the recent work of Battistuzzi et al. [2023] who showed that cyanobacteria could comfortably adapt to the the light typical of M-dwarf stars. Moreover, they used a sophisticated starlight simulator setup which models atmospheric attenuation of light, meaning their cyanobacteria were likely subject to ever scanter illumination than we consider here. Interestingly, they also considered pure “far red” (700−800 nm) illumination and found that this retarded growth rate relative to the M-dwarf light, implying that, as in our model, the organism was adapting its antenna to intercept more photons in the depleted PAR region.It should be noted that they also considered on the red-adapted strains described in the introduction that fared equally well in M-dwarf and far red light. Strictly, both our modelling and the experimental work of Kolodny et al. [2022]. concerns the acclimation of an existing antenna to an unusual lightenvironment rather than the ground-up evolution of an antenna structure specifically optimized to it. Nevertheless, Kolodny’s work demonstrates that oxygenic photosynthesis is, in principle, possible around very low mass stars and our findings indicate that the key consideration is overcoming a fundamental entropic barrier to light-harvesting. This paper is available on arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. available on arxiv

Thermodynamic Limits Around M-dwarf Stars: Discussion 

Authors:
(1) Scott Conn, California Institute of Technology, Pasadena, California;
(2) Joseph Fitzgerald, California Institute of Technology, Pasadena, California;
(3) Jorn Callies, California Institute of Technology, Pasadena, California. Table of Links Abstract and Intro Observations Models Results Discussion Conclusion APPENDIX A APPENDIX B APPENDIX C References References Alford, M. H., 2001: Internal swell generation: The spatial distribution of energy flux from the wind to mixed layer near-inertial motions. Journal of Physical Oceanography, 31 (8), 2359–2368. Alford, M. H., 2020: Revisiting near-inertial wind work: Slab models, relative stress, and mixed layer deepening. Journal of Physical Oceanography, 50 (11), 3141–3156. Alford, M. H., J. A. MacKinnon, H. L. Simmons, and J. D. Nash, 2016: Near-inertial internal gravity waves in the ocean. Annual review of marine science, 8, 95–123. Arbic, B. K., and G. R. Flierl, 2004: Baroclinically unstable geostrophic turbulence in the limits of strong and weak bottom ekman friction: Application to midocean eddies. Journal of Physical Oceanography, 34 (10), 2257–2273. Asselin, O., and W. R. Young, 2020: Penetration of wind-generated near-inertial waves into a turbulent ocean. Journal of Physical Oceanography, 50 (6), 1699–1716. Balmforth, N., S. G. Llewellyn Smith, and W. Young, 1998: Enhanced dispersion of near-inertial waves in an idealized geostrophic flow. Journal of marine research, 56 (1), 1–40. Balmforth, N. J., and W. R. Young, 1999: Radiative damping of near-inertial oscillations in the mixed layer. Journal of marine research, 57 (4), 561–584. Buckingham, C. E., and Coauthors, 2016: Seasonality of submesoscale flows in the ocean surface boundary layer. Geophysical Research Letters, 43 (5), 2118–2126. Burns, K. J., G. M. Vasil, J. S. Oishi, D. Lecoanet, and B. P. Brown, 2020: Dedalus: A flexible framework for numerical simulations with spectral methods. Phys. Rev. Res., 2, 023 068. Callies, J., R. Barkan, and A. N. Garabato, 2020: Time scales of submesoscale flow inferred from a mooring array. Journal of Physical Oceanography, 50 (4), 1065–1086. Damerell, G. M., K. J. Heywood, D. Calvert, A. L. Grant, M. J. Bell, and S. E. Belcher, 2020: A comparison of five surface mixed layer models with a year of observations in the north atlantic. Progress in Oceanography, 187, 102 316. Damerell, G. M., K. J. Heywood, A. F. Thompson, U. Binetti, and J. Kaiser, 2016: The vertical structure of upper ocean variability at the porcupine abyssal plain during 2012–2013. Journal of Geophysical Research: Oceans, 121 (5), 3075–3089. D’Asaro, E. A., 1985: The energy flux from the wind to near-inertial motions in the surface mixed layer. Journal of Physical Oceanography, 15 (8), 1043–1059. D’Asaro, E. A., 1995: Upper-ocean inertial currents forced by a strong storm. Part III: Interaction of inertial currents and mesoscale eddies. Journal of physical oceanography, 25 (11), 2953–2958. D’Asaro, E. A., C. C. Eriksen, M. D. Levine, P. Niiler, P. Van Meurs, and Coauthors, 1995: Upperocean inertial currents forced by a strong storm. Part I: Data and comparisons with linear theory. Journal of Physical Oceanography, 25 (11), 2909–2936. Dewar, W. K., and G. R. Flierl, 1987: Some effects of the wind on rings. Journal of Physical Oceanography, 17 (10), 1653–1667. Essink, S., E. Kunze, R.-C. Lien, R. Inoue, and S.-i. Ito, 2022: Near-inertial wave interactions and turbulence production in a kuroshio anticyclonic eddy. Journal of Physical Oceanography, 52 (11), 2687–2704. Ferrari, R., and C. Wunsch, 2009: Ocean circulation kinetic energy: Reservoirs, sources, and sinks. Annual Review of Fluid Mechanics, 41, 253–282. Flexas, M. M., A. F. Thompson, H. S. Torres, P. Klein, J. T. Farrar, H. Zhang, and D. Menemenlis, 2019: Global estimates of the energy transfer from the wind to the ocean, with emphasis on near-inertial oscillations. Journal of Geophysical Research: Oceans, 124 (8), 5723–5746. Gill, A. E., 1984: On the behavior of internal waves in the wakes of storms. Journal of Physical Oceanography, 14 (7), 1129–1151. 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Hall, 2016: Modulation of wind work by oceanic current interaction with the atmosphere. Journal of Physical Oceanography, 46 (6), 1685–1704. Rocha, C. B., G. L. Wagner, and W. R. Young, 2018: Stimulated generation: extraction of energy from balanced flow by near-inertial waves. Journal of Fluid Mechanics, 847, 417–451. Taburet, G., A. Sanchez-Roman, M. Ballarotta, M.-I. Pujol, J.-F. Legeais, F. Fournier, Y. Faugere, and G. Dibarboure, 2019: Duacs dt2018: 25 years of reprocessed sea level altimetry products. Ocean Science, 15 (5), 1207–1224. Thomas, L. N., L. Rainville, O. Asselin, W. R. Young, J. Girton, C. B. Whalen, L. Centurioni, and V. Hormann, 2020: Direct observations of near-inertial wave 𝜁-refraction in a dipole vortex. Geophysical Research Letters, 47 (21), e2020GL090 375. Thompson, A. F., A. Lazar, C. Buckingham, A. C. N. Garabato, G. M. Damerell, and K. J. Heywood, 2016: Open-ocean submesoscale motions: A full seasonal cycle of mixed layer instabilities from gliders. Journal of Physical Oceanography, 46 (4), 1285–1307. von Storch, J.-S., and V. L¨uschow, 2023: Wind power input to ocean near-inertial waves diagnosed from a 5-km global coupled atmosphere-ocean general circulation model. Journal of Geophysical Research: Oceans, 128 (2), e2022JC019 111. Wagner, G., and W. Young, 2016: A three-component model for the coupled evolution of near-inertial waves, quasi-geostrophic flow and the near-inertial second harmonic. Journal of Fluid Mechanics, 802, 806–837. Wunsch, C., and R. Ferrari, 2004: Vertical mixing, energy, and the general circulation of the oceans. Annu. Rev. Fluid Mech., 36, 281–314. Xie, J.-H., and J. Vanneste, 2015: A generalised-lagrangian-mean model of the interactions between near-inertial waves and mean flow. Journal of Fluid Mechanics, 774, 143–169. Young, W., and M. Ben Jelloul, 1997: Propagation of near-inertial oscillations through a geostrophic flow. JMR, 55, 735–766. Yu, X., A. C. Naveira Garabato, C. Vic, J. Gula, A. C. Savage, J. Wang, A. F. Waterhouse, and J. A. MacKinnon, 2022: Observed equatorward propagation and chimney effect of near-inertial waves in the midlatitude ocean. Geophysical Research Letters, 49 (13), e2022GL098 522. Zhai, X., H. L. Johnson, and D. P. Marshall, 2010: Significant sink of ocean-eddy energy near western boundaries. Nature Geoscience, 3 (9), 608–612. This paper is available on arxiv under CC 4.0 license. Authors: (1) Scott Conn, California Institute of Technology, Pasadena, California; (2) Joseph Fitzgerald, California Institute of Technology, Pasadena, California; (3) Jorn Callies, California Institute of Technology, Pasadena, California. Authors: Authors: (1) Scott Conn, California Institute of Technology, Pasadena, California; (2) Joseph Fitzgerald, California Institute of Technology, Pasadena, California; (3) Jorn Callies, California Institute of Technology, Pasadena, California. Table of Links Abstract and Intro Abstract and Intro Observations Observations Models Models Results Results Discussion Discussion Conclusion Conclusion APPENDIX A APPENDIX A APPENDIX B APPENDIX B APPENDIX C APPENDIX C References References References Alford, M. H., 2001: Internal swell generation: The spatial distribution of energy flux from the wind to mixed layer near-inertial motions. Journal of Physical Oceanography, 31 (8), 2359–2368. Alford, M. H., 2020: Revisiting near-inertial wind work: Slab models, relative stress, and mixed layer deepening. Journal of Physical Oceanography, 50 (11), 3141–3156. Alford, M. H., J. A. MacKinnon, H. L. Simmons, and J. D. Nash, 2016: Near-inertial internal gravity waves in the ocean. Annual review of marine science, 8, 95–123. Arbic, B. K., and G. R. Flierl, 2004: Baroclinically unstable geostrophic turbulence in the limits of strong and weak bottom ekman friction: Application to midocean eddies. Journal of Physical Oceanography, 34 (10), 2257–2273. Asselin, O., and W. R. Young, 2020: Penetration of wind-generated near-inertial waves into a turbulent ocean. Journal of Physical Oceanography, 50 (6), 1699–1716. Balmforth, N., S. G. Llewellyn Smith, and W. Young, 1998: Enhanced dispersion of near-inertial waves in an idealized geostrophic flow. Journal of marine research, 56 (1), 1–40. Balmforth, N. J., and W. R. Young, 1999: Radiative damping of near-inertial oscillations in the mixed layer. Journal of marine research, 57 (4), 561–584. Buckingham, C. E., and Coauthors, 2016: Seasonality of submesoscale flows in the ocean surface boundary layer. Geophysical Research Letters, 43 (5), 2118–2126. Burns, K. J., G. M. Vasil, J. S. Oishi, D. Lecoanet, and B. P. Brown, 2020: Dedalus: A flexible framework for numerical simulations with spectral methods. Phys. Rev. Res., 2, 023 068. Callies, J., R. Barkan, and A. N. Garabato, 2020: Time scales of submesoscale flow inferred from a mooring array. Journal of Physical Oceanography, 50 (4), 1065–1086. Damerell, G. M., K. J. Heywood, D. Calvert, A. L. Grant, M. J. Bell, and S. E. Belcher, 2020: A comparison of five surface mixed layer models with a year of observations in the north atlantic. Progress in Oceanography, 187, 102 316. Damerell, G. M., K. J. Heywood, A. F. Thompson, U. Binetti, and J. Kaiser, 2016: The vertical structure of upper ocean variability at the porcupine abyssal plain during 2012–2013. Journal of Geophysical Research: Oceans, 121 (5), 3075–3089. D’Asaro, E. A., 1985: The energy flux from the wind to near-inertial motions in the surface mixed layer. Journal of Physical Oceanography, 15 (8), 1043–1059. D’Asaro, E. A., 1995: Upper-ocean inertial currents forced by a strong storm. Part III: Interaction of inertial currents and mesoscale eddies. Journal of physical oceanography, 25 (11), 2953–2958. D’Asaro, E. A., C. C. Eriksen, M. D. Levine, P. Niiler, P. Van Meurs, and Coauthors, 1995: Upperocean inertial currents forced by a strong storm. Part I: Data and comparisons with linear theory. Journal of Physical Oceanography, 25 (11), 2909–2936. Dewar, W. K., and G. R. Flierl, 1987: Some effects of the wind on rings. Journal of Physical Oceanography, 17 (10), 1653–1667. Essink, S., E. Kunze, R.-C. Lien, R. Inoue, and S.-i. Ito, 2022: Near-inertial wave interactions and turbulence production in a kuroshio anticyclonic eddy. Journal of Physical Oceanography, 52 (11), 2687–2704. Ferrari, R., and C. Wunsch, 2009: Ocean circulation kinetic energy: Reservoirs, sources, and sinks. Annual Review of Fluid Mechanics, 41, 253–282. Flexas, M. M., A. F. Thompson, H. S. Torres, P. Klein, J. T. Farrar, H. Zhang, and D. Menemenlis, 2019: Global estimates of the energy transfer from the wind to the ocean, with emphasis on near-inertial oscillations. Journal of Geophysical Research: Oceans, 124 (8), 5723–5746. Gill, A. 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Heywood, 2016: Open-ocean submesoscale motions: A full seasonal cycle of mixed layer instabilities from gliders. Journal of Physical Oceanography, 46 (4), 1285–1307. von Storch, J.-S., and V. L¨uschow, 2023: Wind power input to ocean near-inertial waves diagnosed from a 5-km global coupled atmosphere-ocean general circulation model. Journal of Geophysical Research: Oceans, 128 (2), e2022JC019 111. Wagner, G., and W. Young, 2016: A three-component model for the coupled evolution of near-inertial waves, quasi-geostrophic flow and the near-inertial second harmonic. Journal of Fluid Mechanics, 802, 806–837. Wunsch, C., and R. Ferrari, 2004: Vertical mixing, energy, and the general circulation of the oceans. Annu. Rev. Fluid Mech., 36, 281–314. Xie, J.-H., and J. Vanneste, 2015: A generalised-lagrangian-mean model of the interactions between near-inertial waves and mean flow. Journal of Fluid Mechanics, 774, 143–169. Young, W., and M. Ben Jelloul, 1997: Propagation of near-inertial oscillations through a geostrophic flow. JMR, 55, 735–766. Yu, X., A. C. Naveira Garabato, C. Vic, J. Gula, A. C. Savage, J. Wang, A. F. Waterhouse, and J. A. MacKinnon, 2022: Observed equatorward propagation and chimney effect of near-inertial waves in the midlatitude ocean. Geophysical Research Letters, 49 (13), e2022GL098 522. Zhai, X., H. L. Johnson, and D. P. Marshall, 2010: Significant sink of ocean-eddy energy near western boundaries. Nature Geoscience, 3 (9), 608–612. This paper is available on arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. available on arxiv

Want to Learn More About the Interactions Between Near-Inertial Waves and Mesoscale Eddies?

This paper is available on arxiv under CC 4.0 license.
Authors:
(1) Vitor da Fonseca, Instituto de Astrof´ısica e Ciˆencias do Espa¸co, Faculdade de Ciˆencias da Universidade de Lisboa;
(2) Tiago Barreiro, Instituto de Astrof´ısica e Ciˆencias do Espa¸co, Faculdade de Ciˆencias da Universidade de Lisboa and 2ECEO, Universidade Lus´ofona;
(3)Nelson J. Nunes, Instituto de Astrof´ısica e Ciˆencias do Espa¸co, Faculdade de Ciˆencias da Universidade de Lisboa. Table of Links Abstract and Intro
Coupling Dark Energy to Neutrinos
Impact of the Coupling on Perturbations and Observables
Parameter Estimation
Discussion
Acknowledgment, Appendix, and References II. COUPLING DARK ENERGY TO NEUTRINOS Let us consider a flat universe with vanishing curvature, spatially homogeneous and isotropic, whose expansion is parameterized by the scale factor a associated with the Friedmann-Lemaˆıtre-Roberson-Walker (FLRW) spacetime metric. Further considering that the expansion is sourced by photons (γ), baryons (b), cold dark matter (c), neutrinos (ν) and a scalar field dark energy (ϕ) responsible for the current acceleration, the Friedmann equation reads In this study, we want to test a possible interaction between neutrino species and dark energy, in a mass-varying neutrino model where active neutrinos are coupled to the scalar field [13–20]. Because to leading order cosmological data are only sensitive to the total neutrino mass [36, 37], we assume for practical purposes [38] two massless neutrinos and a massive neutrino non-minimally coupled to the quintessence component. The coupled neutrino has a varying effective mass, which depends on the value of the scalar field and on a dimensionless and constant parameter β, The stress energy tensors of the neutrino fluid and the scalar field are not conserved separately. We have where pϕ is the pressure in the field. The extra source terms vanish without interaction, β = 0, or if the massive neutrino particles are ultrarelativistic, behaving as traceless radiation. To test the model with observations, we adopt a known phenomenological parametrization, first proposed in Ref. [22], where the scalar field depends linearly on the number of e-folds, N ≡ ln a, throughout the cosmological evolution. We introduce a dimensionless constant λ for the slope of the scaling: This simple approach is a powerful alternative to the popular CPL parametrization [40, 41], since a large variety of dark energy equation of state evolutions can be captured by just one additional parameter [42], thereby limiting the degeneracies in Bayesian inferences. An additional advantage is that the scalar field potential can be reconstructed analytically following Ref. [22, 24–26]. This is done by solving the first-order differential equation (2.7) to find ρϕ using the constraint equation (2.1) and noting that ϕ˙ = λH according to Eq. (2.9). The potential happens to be a sum of exponential terms, where the mass scales are given by the following analytical expressions, We can see from Fig. 2 that the coupling with neutrinos changes wϕ during the matter-dominated era. For growing masses (β > 0, dotted line), the field equation of state is smaller compared to the uncoupled case (β = 0, solid line). On the contrary, wϕ is larger when the energy transfer occurs in the opposite direction, i.e. from neutrinos of shrinking mass (β < 0, dash-dotted line). Correspondingly, Fig. 3 shows that the non-relativistic neutrinos which receive energy from the scalar field (β > 0) have lower fractional energy density to reach the same present mass than when they give energy (β < 0). with where ϵ is the neutrino comoving energy. This paper is available on arxiv under CC 4.0 license. Authors: (1) Vitor da Fonseca, Instituto de Astrof´ısica e Ciˆencias do Espa¸co, Faculdade de Ciˆencias da Universidade de Lisboa; (2) Tiago Barreiro, Instituto de Astrof´ısica e Ciˆencias do Espa¸co, Faculdade de Ciˆencias da Universidade de Lisboa and 2ECEO, Universidade Lus´ofona; (3)Nelson J. Nunes, Instituto de Astrof´ısica e Ciˆencias do Espa¸co, Faculdade de Ciˆencias da Universidade de Lisboa. This paper is available on arxiv under CC 4.0 license. Authors: Authors: (1) Vitor da Fonseca, Instituto de Astrof´ısica e Ciˆencias do Espa¸co, Faculdade de Ciˆencias da Universidade de Lisboa; (2) Tiago Barreiro, Instituto de Astrof´ısica e Ciˆencias do Espa¸co, Faculdade de Ciˆencias da Universidade de Lisboa and 2ECEO, Universidade Lus´ofona; (3)Nelson J. Nunes, Instituto de Astrof´ısica e Ciˆencias do Espa¸co, Faculdade de Ciˆencias da Universidade de Lisboa. Table of Links Abstract and Intro Coupling Dark Energy to Neutrinos Impact of the Coupling on Perturbations and Observables Parameter Estimation Discussion Acknowledgment, Appendix, and References Abstract and Intro Abstract and Intro Coupling Dark Energy to Neutrinos Coupling Dark Energy to Neutrinos Impact of the Coupling on Perturbations and Observables Impact of the Coupling on Perturbations and Observables Parameter Estimation Parameter Estimation Discussion Discussion Acknowledgment, Appendix, and References Acknowledgment, Appendix, and References II. COUPLING DARK ENERGY TO NEUTRINOS Let us consider a flat universe with vanishing curvature, spatially homogeneous and isotropic, whose expansion is parameterized by the scale factor a associated with the Friedmann-Lemaˆıtre-Roberson-Walker (FLRW) spacetime metric. Further considering that the expansion is sourced by photons (γ), baryons (b), cold dark matter (c), neutrinos (ν) and a scalar field dark energy (ϕ) responsible for the current acceleration, the Friedmann equation reads In this study, we want to test a possible interaction between neutrino species and dark energy, in a mass-varying neutrino model where active neutrinos are coupled to the scalar field [13–20]. Because to leading order cosmological data are only sensitive to the total neutrino mass [36, 37], we assume for practical purposes [38] two massless neutrinos and a massive neutrino non-minimally coupled to the quintessence component. The coupled neutrino has a varying effective mass, which depends on the value of the scalar field and on a dimensionless and constant parameter β, The stress energy tensors of the neutrino fluid and the scalar field are not conserved separately. We have where pϕ is the pressure in the field. The extra source terms vanish without interaction, β = 0, or if the massive neutrino particles are ultrarelativistic, behaving as traceless radiation. To test the model with observations, we adopt a known phenomenological parametrization, first proposed in Ref. [22], where the scalar field depends linearly on the number of e-folds, N ≡ ln a, throughout the cosmological evolution. We introduce a dimensionless constant λ for the slope of the scaling: This simple approach is a powerful alternative to the popular CPL parametrization [40, 41], since a large variety of dark energy equation of state evolutions can be captured by just one additional parameter [42], thereby limiting the degeneracies in Bayesian inferences. An additional advantage is that the scalar field potential can be reconstructed analytically following Ref. [22, 24–26]. This is done by solving the first-order differential equation (2.7) to find ρϕ using the constraint equation (2.1) and noting that ϕ˙ = λH according to Eq. (2.9). The potential happens to be a sum of exponential terms, where the mass scales are given by the following analytical expressions, We can see from Fig. 2 that the coupling with neutrinos changes wϕ during the matter-dominated era. For growing masses (β > 0, dotted line), the field equation of state is smaller compared to the uncoupled case (β = 0, solid line). On the contrary, wϕ is larger when the energy transfer occurs in the opposite direction, i.e. from neutrinos of shrinking mass (β < 0, dash-dotted line). Correspondingly, Fig. 3 shows that the non-relativistic neutrinos which receive energy from the scalar field (β > 0) have lower fractional energy density to reach the same present mass than when they give energy (β < 0). with where ϵ is the neutrino comoving energy.

Relaxing cosmological constraints on current neutrino masses: Coupling Dark Energy to Neutrinos

বর্তমান নিউট্রিনো ভরের উপর মহাজাগতিক সীমাবদ্ধতা শিথিল করা: নিউট্রিনোতে ডার্ক এনার্জি কাপলিং

Lockerung der kosmologischen Beschränkungen für aktuelle Neutrinomassen: Kopplung von Dunkler Energie an Neutrinos

Relajación de las restricciones cosmológicas sobre las masas actuales de neutrinos: acoplamiento de la energía oscura a los neutrinos

Assouplir les contraintes cosmologiques sur les masses actuelles des neutrinos : coupler l'énergie noire aux neutrinos

वर्तमान न्यूट्रिनो द्रव्यमान पर ब्रह्माण्ड संबंधी बाधाओं को कम करना: डार्क एनर्जी को न्यूट्रिनो से जोड़ना

現在のニュートリノ質量に対する宇宙論的制約の緩和: ダークエネルギーとニュートリノの結合

현재 중성미자 질량에 대한 우주론적 제약 완화: 암흑 에너지를 중성미자에 결합

Relaxando as restrições cosmológicas nas atuais massas de neutrinos: Acoplamento da energia escura aos neutrinos

Ослабление космологических ограничений на текущие массы нейтрино: связь темной энергии с нейтрино

Mevcut Nötrino Kütleleri Üzerindeki Kozmolojik Kısıtlamaların Gevşetilmesi: Karanlık Enerjinin Nötrinolara Bağlanması

Nới lỏng các ràng buộc vũ trụ học đối với khối lượng neutrino hiện tại: Kết hợp Năng lượng tối với neutrino

放宽对当前中微子质量的宇宙学限制：将暗能量与中微子耦合

Authors:
(1) Hans van Haren, NIOZ Royal Netherlands Institute for Sea Research, P.O. Box 59, 1790 AB Den Burg, the Netherlands. Table of Links Abstract and Intro Data Observations Simulating Transition Discussion Conclusions and References Abstract The propagation of inertio-gravity waves (IGW) into the deep-sea is relevant for energy transfer to turbulence where waves break, and thus for redistribution of nutrients, oxygen and suspended matter. In constant stratification, vertical IGW-propagation is readily modelled. In varying stratification, where homogeneous layers alternate with stratified layers, transmission and reflection cause complex patterns. Half-year long moored acoustic Doppler current profiler (ADCP) observations midway between the Balearic Islands and Sardinia in the 2800- m deep Western-Mediterranean Sea occasionally demonstrate a distinct transition, between weakly stratified (N2f) and homogeneous (Nf) layers, of IGW at near-inertial frequencies. Here, N denotes the buoyancy frequency and f the local inertial frequency (vertical Coriolis parameter). The transition in stratification is rather abrupt, within z=25 m and provides an amplitude-reduction of 1.3 for super-inertial motions. Simulations with non-traditional momentum equations involving the horizontal Coriolis parameter fh qualitatively confirm observed IGW-refraction. The observational area is marked by variations in hydrographic characteristics, with abundant mesoscale eddies to the south and dense-water formation to the north of the site during the previous winter. Thus, also transitions occur from deep homogeneous layers into deeper, recently formed stratified ones. Polarization spectra of shear are bound by IGW-limits related to N=f, while current-polarization to 2fh. These frequencies coincide with large-scale buoyancy frequencies independently observed in various layers using shipborne CTD-profiling. Keywords Vertical near-inertial wave propagation; transition between homogeneous and weakly stratified layers; deep Western-Mediterranean; ADCP-observations; non-traditional momentum equations 1 Introduction For the latter area, two observational studies in the southern Algerian sub-basin (van Haren and Millot 2004; 2005) suggested near-inertial IGW-propagation, following un-attenuated passage, across the interface between stratified and homogeneous layers. Near-inertial IGWmotions in homogeneous layers generally have marked rectilinear polarization in the horizontal plane [u, v] and show a large aspect ratio of elevated vertical (over horizontal) velocities w(f)/[u, v](f) = 0.1-1. In stratified layers of the ocean, near-inertial horizontal polarization is much more circular and aspect ratios are only O(0.01-0.001). In convective chimneys of a dense-water formation area, vertical currents are easily distinguished from those at near-inertial frequencies (Voorhis and Webb 1970; Gascard 1973; Schott and Leaman 1991). The former vary more rapidly, O(1 hour) or less, in both frequency and amplitude, and they are much more irregular when registered at a mooring, compared to motions at a particular frequency like f. Although vertical currents associated with deep-water formation have been extensively studied (see review by Marshall and Schott (1999), the importance of relatively large w(f) is not explored yet to its full extent. In this paper, the focus is on w(f) related to near-inertial IGW-propagation, and on homogeneous layers that are much thicker than the typical buoyancy scale O(10-100) m (Fig. 1b). Specifically, the w(f)-transition is studied between stratified and homogeneous layers using observations and a simulation. Also, the relationship is considered between observed spectral IGW characteristics and stratification. This paper is available on arxiv under CC 4.0 license. Authors: (1) Hans van Haren, NIOZ Royal Netherlands Institute for Sea Research, P.O. Box 59, 1790 AB Den Burg, the Netherlands. Authors: Authors: (1) Hans van Haren, NIOZ Royal Netherlands Institute for Sea Research, P.O. Box 59, 1790 AB Den Burg, the Netherlands. Table of Links Abstract and Intro Abstract and Intro Data Data Observations Observations Simulating Transition Simulating Transition Discussion Discussion Conclusions and References Conclusions and References Abstract The propagation of inertio-gravity waves (IGW) into the deep-sea is relevant for energy transfer to turbulence where waves break, and thus for redistribution of nutrients, oxygen and suspended matter. In constant stratification, vertical IGW-propagation is readily modelled. In varying stratification, where homogeneous layers alternate with stratified layers, transmission and reflection cause complex patterns. Half-year long moored acoustic Doppler current profiler (ADCP) observations midway between the Balearic Islands and Sardinia in the 2800- m deep Western-Mediterranean Sea occasionally demonstrate a distinct transition, between weakly stratified (N2f) and homogeneous (Nf) layers, of IGW at near-inertial frequencies. Here, N denotes the buoyancy frequency and f the local inertial frequency (vertical Coriolis parameter). The transition in stratification is rather abrupt, within z=25 m and provides an amplitude-reduction of 1.3 for super-inertial motions. Simulations with non-traditional momentum equations involving the horizontal Coriolis parameter fh qualitatively confirm observed IGW-refraction. The observational area is marked by variations in hydrographic characteristics, with abundant mesoscale eddies to the south and dense-water formation to the north of the site during the previous winter. Thus, also transitions occur from deep homogeneous layers into deeper, recently formed stratified ones. Polarization spectra of shear are bound by IGW-limits related to N=f, while current-polarization to 2fh. These frequencies coincide with large-scale buoyancy frequencies independently observed in various layers using shipborne CTD-profiling. Keywords Vertical near-inertial wave propagation; transition between homogeneous and weakly stratified layers; deep Western-Mediterranean; ADCP-observations; non-traditional momentum equations Keywords 1 Introduction For the latter area, two observational studies in the southern Algerian sub-basin (van Haren and Millot 2004; 2005) suggested near-inertial IGW-propagation, following un-attenuated passage, across the interface between stratified and homogeneous layers. Near-inertial IGWmotions in homogeneous layers generally have marked rectilinear polarization in the horizontal plane [u, v] and show a large aspect ratio of elevated vertical (over horizontal) velocities w(f)/[u, v](f) = 0.1-1. In stratified layers of the ocean, near-inertial horizontal polarization is much more circular and aspect ratios are only O(0.01-0.001). In convective chimneys of a dense-water formation area, vertical currents are easily distinguished from those at near-inertial frequencies (Voorhis and Webb 1970; Gascard 1973; Schott and Leaman 1991). The former vary more rapidly, O(1 hour) or less, in both frequency and amplitude, and they are much more irregular when registered at a mooring, compared to motions at a particular frequency like f. Although vertical currents associated with deep-water formation have been extensively studied (see review by Marshall and Schott (1999), the importance of relatively large w(f) is not explored yet to its full extent. In this paper, the focus is on w(f) related to near-inertial IGW-propagation, and on homogeneous layers that are much thicker than the typical buoyancy scale O(10-100) m (Fig. 1b). Specifically, the w(f)-transition is studied between stratified and homogeneous layers using observations and a simulation. Also, the relationship is considered between observed spectral IGW characteristics and stratification. This paper is available on arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. available on arxiv

Near-inertial wave propagation between stratified and homogeneous layers: Abstract and Intro

Entropy, a concept rooted in thermodynamics, has evolved to become a cornerstone across various scientific disciplines, ranging from physics, information theory, coding, and even philosophy. Its diverse applications and implications have led to its recognition as a unifying thread that weaves through the fabric of our understanding of the world. In this article, we delve into the multifaceted nature of entropy, exploring its manifestations in different fields, and highlighting the interconnectedness of these perspectives. Why does time appear to have a preferred direction, flowing from past to future? How did life arise from a primordial soup of molecules? What happens if we don’t spend the time (and energy) necessary to maintain our software code? What is information and how can we communicate over long distances? Can we unravel the complexities of Earth's climate system and predict its future behaviour? What influences wealth distribution and economic equilibrium in societies? Does entropy influence machine learning? Why is genetic diversity important for the survival of species? How can we predict the spontaneity of chemical reactions and phase transitions? How can we explain the tendency of political systems and institutions to become more complex, bureaucratic, and less responsive to the needs of citizens over time? What is the true nature of quantum entanglement and uncertainty? Entropy plays a central role in the answer of each and every question above. Bear in mind though, that this is just a sample of questions touching just a sample of fields. Entropy has a rigorous mathematical definition. It’s such a powerful and universal concept that it is also used metaphorically to clarify multidimensional phenomena. The number of scientific fields that entropy can be found is breathtaking. Here is a short list that is definitely not exhaustive: Thermodynamics, information theory and coding, engineering, software development, economics, social sciences, chemistry, biology, genetics, environmental sciences, cosmology, statistical mechanics, linguistics, sociology, AI, systems theory, earth sciences, ecology and political science. Thermodynamics and Physics Entropy is a central concept in thermodynamics, describing the tendency of energy to spread and systems to evolve towards a state of maximum disorder. The second law of thermodynamics states that the total entropy of an isolated system will always increase over time. This principle has applications in fields like heat engines, refrigeration, and energy transfer. So, why does time appear to have a preferred direction, flowing from past to future? The tendency of systems to evolve toward states of higher disorder shapes our experience of time's irreversible march forward. This deep connection between entropy, the arrow of time, and the evolution of the universe offers a profound insight into the nature of reality itself. Life from a primordial soup of molecules Imagine a pot of water boiling on a stove. As the water heats up, its molecules move around more and more vigorously. Now, think of the molecules in this "primordial soup" as small building blocks. These building blocks are floating around in a mixture of water and other simple ingredients. Entropy comes into play because it's like a natural tendency for things to become more mixed up and spread out over time. In the pot of boiling water, the molecules are bouncing around and spreading out because of the heat. Similarly, in the primordial soup, the molecules are moving around randomly due to their own energy and the heat in the environment. Now, some of these molecules might stick together by chance. Maybe two or more of them connect in just the right way to form something new. These new structures could be more complex molecules, a bit like LEGO pieces snapping together. Some of these structures might end up being the basic building blocks of life, like the bricks in a LEGO creation. Over a really long time, with lots of random mixing and connecting, some of these structures might become even more complex and organised. This is where entropy comes into play again. Even though the overall entropy of the universe tends to increase, locally, in small parts of the universe, things can become more ordered if they absorb energy from their surroundings. Just like how a snowflake forms even though the environment is getting messier, these organised structures can form and grow. Software development Systems tend to naturally evolve towards states of higher disorder unless energy is invested to maintain or improve their order. There is a metaphor in software systems that prompts software developers to invest their energy for building quality software. If a codebase is not regularly cleaned up, refactored, and improved, it can become increasingly disorganised, complex, and difficult to understand and maintain. Software programmers should actively fight against software entropy. This involves consistently refactoring and cleaning up the codebase, removing duplication, simplifying complex parts, and adhering to good coding practices. So, what happens if we don’t spend the time (and energy) necessary to maintain our software code? Our code’s entropy rises which is bad news for its maintainability. Information theory, channel coding and source encoding Entropy, often denoted as "H(X)", measures the uncertainty or randomness associated with a random variable X. In the context of information theory, entropy quantifies the amount of information contained in a random variable. If a random variable has high entropy, it means that the variable takes on a wide range of values, and thus carries a lot of information. Conversely, if the entropy is low, it means the variable is more predictable and carries less information. Channel coding deals with sending information reliably over a noisy communication channel. Entropy plays a role here through the "Shannon's Channel Coding Theorem." This theorem states that for a given communication channel with a certain capacity, it is possible to transmit information at rates up to the channel's capacity without errors, provided the code rate (the ratio of information bits to total transmitted bits) is below this capacity. The concept of entropy comes into play because the channel capacity is closely related to the channel's noise level, which affects the uncertainty or entropy of the received signal. Source encoding (also known as data compression) is the process of representing information in a more efficient manner. Entropy is directly related to the minimum average number of bits needed to represent symbols from a given source. This is known as the "Shannon's Source Coding Theorem," which states that any lossless compression scheme cannot compress data to a size smaller than the entropy of the source. In simpler terms, if the entropy of a source is "H(X)" bits per symbol, then no compression scheme can achieve an average coding length of less than "H(X)" bits per symbol while preserving all the information. So, what is information and how can we communicate over long distances? Information is the amount of uncertainty and it is measured in entropy. To communicate over long distances we may use channel coding and source encoding (among others). Earth’s climate The Earth's climate system is a highly complex and dynamic system influenced by a multitude of factors, including atmospheric composition, ocean currents, solar radiation, greenhouse gasses, and more. While our understanding of the climate system has improved significantly over the years, predicting its future behaviour with absolute certainty remains a challenging task due to the system's inherent complexity and the presence of various feedback mechanisms. So, can we unravel the complexities of Earth's climate system and predict its future behaviour? Entropy can help us understand certain aspects of the system's behaviour. The increase in entropy is associated with irreversible processes, such as energy transformations that result in the dissipation of energy in the form of heat. In the context of earth's climate, the increase in greenhouse gas concentrations leads to an increase in the absorption and retention of heat, resulting in temperature changes. This can be seen as a form of irreversible process that contributes to the overall entropy change in the climate system. Climate feedback mechanisms involve complex interactions between different components of the climate system. Positive feedback loops can amplify initial changes, leading to further changes in the system. For instance, as ice melts due to warming temperatures, it reduces the earth's albedo (reflectivity), which in turn leads to more heat absorption and further warming. These feedback mechanisms can lead to increases in entropy within the climate system. The concept of entropy highlights the idea that complex systems tend to evolve toward states of higher entropy, which can correspond to greater disorder. In the case of the climate system, its complexity makes it challenging to predict exact future outcomes due to the interactions and feedback that can lead to unpredictable behaviour. Economy Economics involve human behaviour, social structures, policy decisions, and a wide range of dynamic factors that interact in complex ways. One lens among many used to analyse and model economic systems is entropy. Wealth distribution refers to how wealth is allocated among individuals or households. Entropy, in this context, can be thought of as a measure of the level of inequality in wealth distribution. When wealth is evenly distributed among all members of a society, the "economic entropy" is low, indicating a state of order. However, as wealth becomes concentrated in the hands of a few, economic entropy increases, suggesting greater disorder or inequality. Economic equilibrium refers to a state where supply and demand are balanced, and there is no incentive for participants to change their behaviour. In a metaphorical sense, this state of equilibrium could be seen as a state of lower economic entropy, where resources are efficiently allocated and economic activity is stable. If the economy experiences sudden shocks or imbalances, it can lead to changes in economic entropy as the system readjusts to a new equilibrium. So, what influences wealth distribution and economic equilibrium in societies? Market dynamics. They include factors such as competition, innovation, and consumer behaviour, that can influence the distribution of wealth and economic equilibrium. In a competitive market, wealth tends to flow towards those who provide valuable goods and services, potentially leading to changes in wealth distribution. Market innovations and disruptions can also impact economic equilibrium and wealth distribution, causing shifts in economic entropy. Machine learning Entropy is a fundamental concept in machine learning, for example, in decision tree algorithms. It serves as a measure of uncertainty or disorder in data, enabling algorithms to quantify the impurity of subsets or distributions. In decision trees, entropy is utilised to determine the best feature for data splitting, leading to optimal classification. Additionally, entropy-based metrics such as information gain guide the process of feature selection, enhancing model accuracy. In clustering algorithms, entropy is used to assess the homogeneity of clusters. Overall, entropy empowers machine learning models to make informed decisions, enabling them to efficiently learn from and interpret complex datasets. So, does entropy influence machine learning? Yes it does. Genetic diversity Genetic diversity refers to the variety of genetic traits and variations present within a population of a species. This diversity is the result of mutations, recombination, and genetic drift over generations. When a species exhibits high genetic diversity, it means that different individuals possess various combinations of genes, increasing the chances that some of them will possess advantageous traits for surviving and reproducing in different conditions. Higher genetic diversity equates to higher entropy within a population's genetic information. This increased entropy signifies the richness of genetic possibilities and potential adaptations. A low-entropy scenario, with very limited genetic diversity, may lead to a lack of adaptive responses, making the population more vulnerable to changes in the environment. So, why is genetic diversity important for the survival of species? Higher genetic diversity results in higher entropy within a population's genetic information. This increases the chances of survival of species. Chemical reactions The spontaneity of chemical reactions and phase transitions is determined by the concept of Gibbs free energy (G) and its relationship with entropy (S) and enthalpy (H). The Gibbs free energy change (ΔG) for a process indicates whether the process will occur spontaneously at a given temperature and pressure. So, how can we predict the spontaneity of chemical reactions and phase transitions? Entropy is essential in predicting the spontaneity of chemical reactions and phase transitions because it provides information about the degree of disorder or randomness in a system. Processes that lead to an increase in entropy tend to be favoured, but the interplay between entropy and enthalpy, along with the temperature factor, determines whether a process will actually occur spontaneously. Political systems As political systems and institutions grow in size and scope, they often develop bureaucratic structures to manage the increasing complexity. Bureaucracy involves the creation of layers of hierarchy, standardized procedures, and specialized divisions to handle various tasks. This complexity is intended to improve efficiency, coordination, and decision-making. However, bureaucracy can also lead to rigid procedures, slow decision-making, and reduced responsiveness to changing citizen needs. So, how can we explain the tendency of political systems and institutions to become more complex, bureaucratic, and less responsive to the needs of citizens over time? The answer comes from entropy in systems theory. As these systems evolve, entropy increases. They accumulate layers of complexity, regulations, and specialized structures, which can hinder adaptability and responsiveness. This lack of adaptability, responsiveness and efficiency is a form of entropy, where the system becomes increasingly resistant to change. Quantum level Quantum entanglement refers to a phenomenon where the quantum states of two or more particles become correlated in such a way that the state of one particle cannot be described independently of the state of the other particle(s). This means that even when particles are separated by large distances, the properties of one particle instantaneously affect the properties of the other, violating classical notions of locality and causality. Quantum entanglement and uncertainty are fundamental concepts in quantum mechanics that reveal the intriguing and counterintuitive nature of the quantum world. These concepts challenge our classical intuitions and play a crucial role in understanding the behaviour of particles and systems at the quantum level. Entropy, in both classical and quantum contexts, is a measure of disorder, randomness, or information content. In quantum mechanics, entropy is used to quantify the uncertainty or lack of information about a quantum state. So, what is the true nature of quantum entanglement and uncertainty? They are deeply intertwined with the concept of entropy, as they involve the measurement, sharing, and exchange of information among particles or systems. Wrapping Up The beauty of entropy lies in its ability to bridge seemingly unrelated scientific disciplines. The connections between entropy in physics, chemistry, biology, information theory, and other fields highlight its universal applicability. It demonstrates how fundamental principles underlie diverse natural phenomena and human endeavors. Exploring the manifestations of entropy in these fields, we gain a deeper appreciation for the connections that define the scientific landscape.

Entropy Can Explain Too Much

The are a series of interviews featuring various important voices and perspectives in the Bitcoin ecosystem. Each interviewee was carefully selected and asked the same group of questions. The main goal was to provide the world with a collection of commentary and opinions on the state of the current Bitcoin and crypto market. Some of the names you will recognize while others don’t wish for the limelight but have great insight and experience we all can learn from. Bitcoin Bear Market Diaries These interviews are raw and unfiltered with no agenda other than giving each individual their opportunity to speak their mind. If you like what you see, please share with your friends. If something offends you, you should probably X out and find another crypto fluff piece that gives you warm fuzzies. Apex is a Venezuelan Bitcoiner who understands the value proposition of Bitcoin better than most due to the geo political issues and rapid inflation taking place in his country. Name Apex Country Venezuela/USA How do people know you? @malandrox7 in twitter How long have you been into Bitcoin? December 2016 Best Bitcoin experience? All of 2017 was awesome even with the segwit2x drama Worst Bitcoin experience? There is no such thing as a “worst” bitcoin experience What do you think is Bitcoin’s biggest threat? The only unknown is the possibility of a software bug we are unaware of. With that said, in bitcoin’s 10 year history unanticipated vulnerabilities in the code have been resolved professionally by extraordinary bitcoin devs. What are your thoughts on the various Bitcoin forks? They’ve been great to turn into more bitcoin. Besides that, they are useless spawn. What are you optimistic about in this space? Younger generation of users and developers that will build use cases we can’t even fathom. Just like in 1990 we couldn’t imagine we’d have phone conversations with live video with people on the other side of the globe. Also, improved GUI and safe storage. Biggest regret during the last bull market? No “ragrets”. I guess I could’ve taken out more fiat out but who wants to hold a shitcoin? What have you learned during the current bear market? That if you have a strong understanding of what bitcoin is and what it is capable of, bear markets are a great opportunity to accumulate more bitcoin. What is the biggest fail you have seen during the bear market? The financially uneducated getting their asses handed to them and temporarily letting go of this amazing, once in a lifetime asset. What do you think helped trigger the current bear market? Crypto sweatshirts and crypto nails. What kind of damage do you think latest price drop has done to buyer sentiment? Those that owned bitcoin earlier than myself know that bitcoin was/is a chance for retail investors to get in before institutional investors. Now those retail investors that sold their bitcoin will get their lunch eaten by institutional investors….. again. How do you feel about the current state and future of lightning network? Lightning devs live and breath bitcoin. They are the smartest minds working day and night to create these layered solutions with possibilities of MoE and energy transfer we can’t even wrap our minds around. The future looks amazing. Also, if bitcoin were to remain what it was since its inception it would still serve it’s sound money purpose. What are your thoughts on HODLing Bitcoin? Bitcoin hodlers are creating a legacy for themselves and their families and they don’t even know it. My prediction is that in the next run, “hodl” will be caked into the Merriam-Webster dictionary. What are your thoughts on alt-coins? If people want to trade them to obtain more bitcoin, then by all means… They’d probably have better luck at the slot machines in Vegas since statistically 1 out of 10 traders actually make money in the long term. If it wasn’t for an alt-coin I wouldn’t have gotten into bitcoin. I’ll explain below. Do you hold any? If not, why? My pot dealer is the one that got me into bitcoin. He requested I pay him in Ether and proceeded to give me a crash course on “how it works”. Coming from a financial background I was immediately intrigued and hooked. I think because of my education in finance within a couple of weeks I quickly determined that bitcoin is the only cryptocurrency that mattered. All my cryptocurrency research went into bitcoin and is the only one I own. My pot dealer solely owns bitcoin now because of our induced, meditative conversations. ;) What kind of impact do you think the radical drop in alt-coins will have on their future? Honestly, I do not know and can give a rats ass. Thoughts on the notion of bitcoinization? Due to the economics of bitcoin I think it’s inevitable. At a core level, the worldwide populace has lost trust in our financial system. Bitcoin is an alternative to all that is corrupt and wrong with what your readers and followers already know. What Bitcoin startups are you excited about? Anything that @beautyon is involved in. This guy gets it and I encourage everyone to follow him. I’ve learned a lot just by following him. Azteco is his company. What “crypto influencers” do you think get it wrong and why? To me it’s not so much about the influencers as it is about the people that choose to consume their content. It’s a free market and people have the right to follow, read and view whoever they want. However, do so at your own discretion. Personally my little echochamber makes me more knowledgeable everyday. What “crypto influencer” do you think gets it right and why? See above. What’s it going to take for this bear market to turn around? Once I cut my hair, but I’m not done accumulating so everyone will have to wait. How bullish are you on Bitcoin despite this recent pullback? I have been completely unphased by this pullback. I’m a perma bull in life and in bitcoin. Any tips you want to give to people new to Bitcoin? In layman terms, see bitcoin as your savings account. So whatever percentage of your income you set aside for savings put it all into bitcoin and keep on grinding for more. Best tips for storing Bitcoin? Trezor wallet, Casa Hodl if your serious about your legacy. Name some of your favorite information sources and/or podcasts in the space. Adam Meister’s “This week in bitcoin” on YouTube. He has the best guests and everytime I watch I end up #stackingmoresats I’m partial to his show also because he shines a well needed light on the situation of my country. Venezuela. Any last words of wisdom? Invest in your financial education. Unfortunately, education systems around the world do not emphasize this enough. It is up to you to put in the time. Only with a strong financial education can one achieve financial sovereignty. Stay tuned for the next Bear Market Bitcoin Diaries. You can find more volumes and articles here!

Bitcoin Bear Market Diaries Volume 15 with Apex

Just as the individual control of fire changed the balance of power between nature and humans, the individual control of energy to validate the monetization, transfer, and storage of value, changed the balance of power between ordinary citizens and their nation-states. Bitcoin’s Proof of Work turns energy into a generic entry fee to preserve miner anonymity and block-winner unpredictability. This factor prevents anyone from monopolizing Bitcoin’s monetization, transfer, and store of value protocol. As monetary monopoly dies off so does inflation -the hidden tax, it imposes on individual income. SLIDE 2 Energy extraction, conversion, or delivery efficiency confers a decisive advantage in Human Resource Competition Dynamics [RCD1]. Maximizing its value is key to increasing living standards as the global population approaches 8 billion. Today’s most dominant states are the first who identified higher-density energy sources or learned to maximize the efficiency of energy conversion, extraction, or delivery. Likewise, states who adopt Bitcoin’s impregnable autonomy to deploy resources instantly, globally, and inexpensively will become the world’s most energy efficient. SLIDE 3 Bitcoin turns energy into an immutable unit of account by priming individual self-interest to reach simultaneous, secure, and irreversible consensus, prior to registering bookkeeping entries on a ledger, shared among innumerable, unrelated, and globally disseminated parties. Every 10 min. Bitcoin owners get a verified, updated, and auditable copy of the digital ledger that replaces every constraint previously precluding individuals from instantaneously transferring or personally storing their money, without requiring permission from the state or its banking agents. SLIDE 4 By subtracting human control from our civilization’s notional money concept, Bitcoin prevents public and private bureaucrats from seizing and allocating value according to their interests. As ensued recently in VENEZUELA: A country where Keynes’ most popular stealth-confiscation tools (inflation, currency devaluation, and interest rate manipulation) were expressly deployed by the state to embezzle the country’s total annual economic production, plus all excess economic value (savings) previously accrued by private citizens and entities during the 20th century. SLIDE 5 Using a simple Reductio ad Absurdum argument, where Venezuela serves as the “absurdum” every nation-state on earth is likely to finish at, shows why Keynesian economics and central banking are untenably detrimental to human survival. In contrast to fiat money and the deeply centralized abstractions calling themselves “crypto,” Bitcoin’s dominance will spread, as individuals realize it is the only monetary system, whose processes do not depend on anyone’s regulatory permissions, electrical power, human teams, cloud servers, miners, nodes, etc. For instance, as word of Bitcoin spread over the past decade, guess which country reached the world’s fourth-largest Bitcoin trading volume in 2018? -the original year of this post's publication- SLIDE 6 Bitcoin’s algorithm comprises a cluster of first-ever applications of the most innovative, previously unrealized mathematical, digital, financial, and other disciplines’ inventions. One of its peak implementations is a world-changing innovation that adds a sense of finality to the apex monetary system ever created. Triple-Entry Bookkeeping, the accounting system meant to remove Centralized Trust, Double-Entry Bookkeeping’s unavoidable byproduct was not even known until Bitcoin’s activation validated it, 20 years after Tepper Prof. Yuji Ijiri invented it. Bitcoin's equally far-reaching significance is providing the only safe conduit for switching from Second-Entry to Triple-Entry Bookkeeping. The last time civilization met such a change, State and Church split. SLIDE 7 While Single-Entry Bookkeeping started along with civilization 5,000 years ago, Double-Entry Bookkeeping planted the seeds of Capitalism, when Frai Pacioli formalized it in the 15th century. Triple-Entry Bookkeeping (TEB) will revolutionize the world, 500 years later, through Bitcoin. Centralized Trust reached a point beyond which, it could only subsist, under a mantle of central bank monetary maneuvers, collusive practices, and concealed gate-keeping constraints. Yet, it wasn’t until famed cryptographer Ian Grigg issued his 2005 paper, that TEB became known. Four years later, Satoshi put it to work. SLIDE 8 As Bitcoin's coinbase reward and transactional fees motivate potential miners to increase the grid of nodes, network effects increase Bitcoin's difficulty adjustment and make it more expensive to waste resources, confirming invalid ledger entries. In time, whether Bitcoin's price rises or not, grid growth persistently funds a larger asymmetry between the cost of hacking its ledger and the cost of validating it. On top, having no tangible entities to intimidate legally or physically, decidedly increases the likelihood of Bitcoin’s perpetuity. [2] SLIDE 9 Extrinsic factors can centralize any digital ledger, unless 1. It can expand the number of validations and nodes performing them until reaching difficulty levels, high enough to deter attacks, 2. There are no internal human attack surfaces, and 3. Executing a change to its code requires very high consensus levels. Such a ledger would’ve had to expand unseen for years. Its key designer/s would’ve had to fully vanish, and major changes would have already required levels as high as were made necessary by The Blocksize War. Guess which is the only coin in the universe that fits the bill? [3] SLIDE 10 As a 19th-century political genius, philosopher, and scientist, Max Weber said “it is not true that good can follow only from good and evil only from evil, but that often the opposite is true. Anyone who fails to see this is, indeed, a political infant.” Thus, why Galileo, was only recently pardoned by the Church (1992). Like our 15th-century forefathers, one might expect, our current bureaucratic overlords won’t let monetary gains from seigniorage slip away from their grip, without a fight. They will soon find a way to declare it illegal and prosecute citizens for using it. FOOTNOTES [1] RCD (Resource Competition Dynamics) within the context explained here -make sure to check the summary's opinion note. [2] Only an Immutable , Non-Systemic, Individually Controlled currency can efficiently replace Monetary Central Planning. [3] Only Bitcoin fits all three requirements. Just as the individual control of fire changed the balance of power between nature and humans, the individual control of energy to validate the monetization, transfer, and storage of value, changed the balance of power between ordinary citizens and their nation-states. Just as the individual control of fire changed the balance of power between nature and humans, the individual control of energy to validate the monetization, transfer, and storage of value, changed the balance of power between ordinary citizens and their nation-states. Bitcoin’s Proof of Work turns energy into a generic entry fee to preserve miner anonymity and block-winner unpredictability. This factor prevents anyone from monopolizing Bitcoin’s monetization, transfer, and store of value protocol. As monetary monopoly dies off so does inflation -the hidden tax, it imposes on individual income. SLIDE 2 SLIDE 2 Energy extraction, conversion, or delivery efficiency confers a decisive advantage in Human Resource Competition Dynamics [RCD1]. Maximizing its value is key to increasing living standards as the global population approaches 8 billion. Energy extraction, conversion, or delivery efficiency confers a decisive advantage in Human Resource Competition Dynamics [RCD1]. Maximizing its value is key to increasing living standards as the global population approaches 8 billion. Today’s most dominant states are the first who identified higher-density energy sources or learned to maximize the efficiency of energy conversion, extraction, or delivery. Likewise, states who adopt Bitcoin’s impregnable autonomy to deploy resources instantly, globally, and inexpensively will become the world’s most energy efficient. SLIDE 3 SLIDE 3 Bitcoin turns energy into an immutable unit of account by priming individual self-interest to reach simultaneous, secure, and irreversible consensus, prior to registering bookkeeping entries on a ledger, shared among innumerable, unrelated, and globally disseminated parties. Bitcoin turns energy into an immutable unit of account by priming individual self-interest to reach simultaneous, secure, and irreversible consensus, prior to registering bookkeeping entries on a ledger, shared among innumerable, unrelated, and globally disseminated parties. Every 10 min. Bitcoin owners get a verified, updated, and auditable copy of the digital ledger that replaces every constraint previously precluding individuals from instantaneously transferring or personally storing their money, without requiring permission from the state or its banking agents. SLIDE 4 SLIDE 4 By subtracting human control from our civilization’s notional money concept, Bitcoin prevents public and private bureaucrats from seizing and allocating value according to their interests. As ensued recently in VENEZUELA: By subtracting human control from our civilization’s notional money concept, Bitcoin prevents public and private bureaucrats from seizing and allocating value according to their interests. As ensued recently in VENEZUELA: A country where Keynes’ most popular stealth-confiscation tools (inflation, currency devaluation, and interest rate manipulation) were expressly deployed by the state to embezzle the country’s total annual economic production, plus all excess economic value (savings) previously accrued by private citizens and entities during the 20th century. SLIDE 5 SLIDE 5 Using a simple Reductio ad Absurdum argument, where Venezuela serves as the “absurdum” every nation-state on earth is likely to finish at, shows why Keynesian economics and central banking are untenably detrimental to human survival. Using a simple Reductio ad Absurdum argument, where Venezuela serves as the “absurdum” every nation-state on earth is likely to finish at, shows why Keynesian economics and central banking are untenably detrimental to human survival. In contrast to fiat money and the deeply centralized abstractions calling themselves “crypto,” Bitcoin’s dominance will spread, as individuals realize it is the only monetary system, whose processes do not depend on anyone’s regulatory permissions, electrical power, human teams, cloud servers, miners, nodes, etc. For instance, as word of Bitcoin spread over the past decade, guess which country reached the world’s fourth-largest Bitcoin trading volume in 2018? -the original year of this post's publication- SLIDE 6 SLIDE 6 Bitcoin’s algorithm comprises a cluster of first-ever applications of the most innovative, previously unrealized mathematical, digital, financial, and other disciplines’ inventions. One of its peak implementations is a world-changing innovation that adds a sense of finality to the apex monetary system ever created. Bitcoin’s algorithm comprises a cluster of first-ever applications of the most innovative, previously unrealized mathematical, digital, financial, and other disciplines’ inventions. One of its peak implementations is a world-changing innovation that adds a sense of finality to the apex monetary system ever created. Triple-Entry Bookkeeping, the accounting system meant to remove Centralized Trust, Double-Entry Bookkeeping’s unavoidable byproduct was not even known until Bitcoin’s activation validated it, 20 years after Tepper Prof. Yuji Ijiri invented it. Tepper Prof. Yuji Ijiri Bitcoin's equally far-reaching significance is providing the only safe conduit for switching from Second-Entry to Triple-Entry Bookkeeping. The last time civilization met such a change, State and Church split. SLIDE 7 SLIDE 7 While Single-Entry Bookkeeping started along with civilization 5,000 years ago, Double-Entry Bookkeeping planted the seeds of Capitalism, when Frai Pacioli formalized it in the 15th century. Triple-Entry Bookkeeping (TEB) will revolutionize the world, 500 years later, through Bitcoin. While Single-Entry Bookkeeping started along with civilization 5,000 years ago, Double-Entry Bookkeeping planted the seeds of Capitalism, when Frai Pacioli formalized it in the 15th century. Triple-Entry Bookkeeping (TEB) will revolutionize the world, 500 years later, through Bitcoin. Centralized Trust reached a point beyond which, it could only subsist, under a mantle of central bank monetary maneuvers, collusive practices, and concealed gate-keeping constraints. Yet, it wasn’t until famed cryptographer Ian Grigg issued his 2005 paper, that TEB became known. Four years later, Satoshi put it to work . Satoshi put it to work SLIDE 8 SLIDE 8 As Bitcoin's coinbase reward and transactional fees motivate potential miners to increase the grid of nodes, network effects increase Bitcoin's difficulty adjustment and make it more expensive to waste resources, confirming invalid ledger entries. As Bitcoin's coinbase reward and transactional fees motivate potential miners to increase the grid of nodes, network effects increase Bitcoin's difficulty adjustment and make it more expensive to waste resources, confirming invalid ledger entries. In time, whether Bitcoin's price rises or not, grid growth persistently funds a larger asymmetry between the cost of hacking its ledger and the cost of validating it. On top, having no tangible entities to intimidate legally or physically, decidedly increases the likelihood of Bitcoin’s perpetuity. [2] [2] SLIDE 9 SLIDE 9 Extrinsic factors can centralize any digital ledger, unless 1. It can expand the number of validations and nodes performing them until reaching difficulty levels, high enough to deter attacks, 2. There are no internal human attack surfaces, and 3. Executing a change to its code requires very high consensus levels. Extrinsic factors can centralize any digital ledger, unless 1. It can expand the number of validations and nodes performing them until reaching difficulty levels, high enough to deter attacks, 2. There are no internal human attack surfaces, and 3. Executing a change to its code requires very high consensus levels. Such a ledger would’ve had to expand unseen for years. Its key designer/s would’ve had to fully vanish, and major changes would have already required levels as high as were made necessary by The Blocksize War . The Blocksize War Guess which is the only coin in the universe that fits the bill? [3] SLIDE 10 SLIDE 10 As a 19th-century political genius, philosopher, and scientist, Max Weber said “it is not true that good can follow only from good and evil only from evil, but that often the opposite is true. Anyone who fails to see this is, indeed, a political infant.” As a 19th-century political genius, philosopher, and scientist, Max Weber said “it is not true that good can follow only from good and evil only from evil, but that often the opposite is true. Anyone who fails to see this is, indeed, a political infant.” Thus, why Galileo, was only recently pardoned by the Church (1992). Like our 15th-century forefathers, one might expect, our current bureaucratic overlords won’t let monetary gains from seigniorage slip away from their grip, without a fight. They will soon find a way to declare it illegal and prosecute citizens for using it. FOOTNOTES FOOTNOTES [1] RCD (Resource Competition Dynamics) within the context explained here -make sure to check the summary's opinion note. [1] within the context explained here [2] Only an Immutable , Non-Systemic, Individually Controlled currency can efficiently replace Monetary Central Planning. [2] [3] Only Bitcoin fits all three requirements. [3]

 The Bitcoin Power Shift 

With concerns about global climate change on the rise, there’s one essential question that remains: Solar panels are increasingly becoming and many communities — even you wouldn’t normally expect them — are looking to the advantages of renewable energy from sources like solar, wind, and hydroelectric. How do we effectively implement renewable energy? more efficient in areas However, although more people are directing their attention to renewable energy as a key component of sustainability and responsible consumption, it may not be enough. Recently, the International Energy Agency published news that renewable energy is . Even with IEA forecasts of renewable energy growing to account for 18 percent of the world’s energy by 2040, that’s still well below their ideal sustainability target of 28 percent. Could blockchain technology offer a solution for more widespread adoption, usage, and integration of renewable energy in a more resilient manner? not growing fast enough to meet climate goals A Centralized System In its current state, there are a variety of issues that plague the energy grids already in place. For starters, one of the biggest flaws is the centralization of power grids. Though having a centralized system may not seem like a flaw at first (streamlined power, right?) the negative aspects of such a system can be substantial to say the least. Given events in recent history, the problems of centralized power grids have now become apparent. If we look to places like or Melbourne, Australia after a recent we see the effects more closely. In both cases, thousands of residents were left without power due to failures in the established energy grids. In both cases, the systems would have failed regardless of the source of energy as the failure was due to the centralized nature of the systems and the lack of resilience and adaptability. Centralized systems also mean . Puerto Rico after Hurricane Maria prolonged heat wave centralized failures Decentralizing the Grid Though there are various solutions proposed for solving the current concerns in how governments are handling energy grids, perhaps the most salient answer is from those calling for decentralization. Laurie Guevara-Stone is with the Rocky Mountain Institute and focuses on questions of renewable and sustainable energy for the future of the globe. In a , Guevara-Stone addressed why systems are a better response to growing concerns. piece for GreenBiz decentralized “But while many approaches to improving the grid’s reliability and resilience have focused on hardening — fortifying important but weak nodes in the system — there is a better way: decentralizing the grid through distributed energy resources. The less centralized a system is, the less prone it is to large-scale failure, a fact that many countries are acting on.” When communities aren’t reliant on centralized sources for their power and methods of accessing that power, the energy grid is able to be far more resilient and we may one day be able to . avoid power outages altogether Why Blockchain? As a quickly-expanding field in the tech sector, it should come as no surprise that blockchain technology is uniquely positioned solution for the energy sector’s issues. With an inherent focus on decentralization and distributed networks, one can plausibly argue that blockchain technology was expressly built for such an application. Governments can take advantage of blockchain technology to start building distributed power grids of their own. With distributed systems, local areas are able to experience greater resiliency, adaptability, and reliability from their power grid. In fact, there are examples of this approach already taking place in the real world right now. For example, the , a project backed by the non-profit AI Grid Foundation, recently raised for the renewable energy initiative and is looking to use that funding to make a difference. The Eloncity Model leverages both blockchain technology and renewable energy sources for a more sustainable future. To ensure the healthy future of the energy sector, Eloncity is providing the blockchain-based means for microgrids and energy transmission. Eloncity Model $20 million in funding In fact, the Eloncity model is already being implemented. In San Juanico, Mexico on the Baja California peninsula, the Foundation is creating a sustainable method for the and improve the capacity for energy transmission. The new initiative is creating a distributed network of microgrids offering a more efficient and responsible model for energy transfer and consumption. local community to have energy Another example of blockchain technology in action in the renewable energy sector is . The Austin-based blockchain startup is taking a different approach and focusing on rewarding those who use energy responsibly and generate renewable energy of their own. Rather than building the infrastructure for more resilient renewable energy, the Swytch team is “using the blockchain to track, verify, and reward sustainability.” Swytch The concept is to create financial incentives for both individuals and businesses to adopt more responsible sources of energy and to reduce their reliance on fossil fuels. This theme of financial incentivization is also applicable to governments looking to implement more sustainable energy systems. Like Swytch and Eloncity, governments can take advantage of distributed energy systems to battle power monopolies in specific areas. If there is a financial incentive for businesses and individuals to make the switch to more responsible energy consumption that is outside the hands of large power companies, then it’s only a matter of time until consumers act in the best interest of not only their well-being but of their wallets. As the renewable energy sector continues to grow, communities, individuals, and governments alike are all looking for proper ways to implement sound rollout strategies. With the advent and implementation of blockchain technology, we may be seeing that sooner, rather than later. The future of the energy sector is two-fold: sustainable and resilient. By combining blockchain technology and renewable energy sources, the industry is in store to accomplish both goals in the not-so-distant future.

Will Blockchain Assist the Search for Renewable Energy Solutions?

From nebulae to neurons, then to the Quantum realm. Bitcoin has rattled some powerful cages. It is prophesized to be the “ ; the “ of the centralized banking elite. So it is evident that in order to be placed and hyped into such a historic trajectory, it needs to be governed by laws and rules that offer good security- a security that can withstand government level interventions, network attacks and the black hat. For you to understand how this security is implemented, you need to understand what is. This security is the backbone of bitcoin. But, somehow, this doesn’t mean that bitcoin is not Hackable. It is susceptible to social engineering and stupidity-induced attack vectors. No matter how secure your home is, if you leave the gates and the doors wide open, you invite a Robbery. ultimate decentralizer” dethroner” hashing SHA256 is the name of the hashing algorithm that governs the hashing in Bitcoin networks. SHA 256 is made up of 256 bits. You already know that your 4 digit ATM PIN is not stored anywhere. Instead, a hash is generated from the 4 digits and that hash is stored in the bank’s database. When you type in your PIN at the time you want to perform some transactions, the ATM machine will produce a hash from the PIN you entered and it will be compared with the hash that is already stored. Unlike in encryption, here, there is actually no correlation between the source data and the resulting hash. The only way the hash can be reversed is by counting all the possibilities that the hash can produce. Which means, you need to find every combination of numbers that a 256 bit address space can produce. Further splitting it down, let’s say you are solving a puzzle and at some step, you are required to find a 4 digit number and put it into the lock of a door that leads you to the next level of the game. You can try as many numbers as possible and the door will only open once the correct number is inserted. The password is binary; that means it consists entirely of 1 and 0s. So you need to find a number that is made up of 1s and 0s. Let’s call these numbers as . bits And you have no clues. You open the door or you die. All you can possibly do, is to manually try every number starting from 0000 to 1111. How many numbers will you have to try, in the worst case? That number is given by the formulae ²⁴=16. So, in the same way, our computers operate in a binary space. It comprehends every data is receives as binary data. Our Bitcoin block chain is represented by a 256 bit hash. To reverse that hash, you will need to try every combination of a 256 bit number. That means, any algorithm, wishing to reverse the 256 bit hash, to produce the origin data has to run permutations on the hash of order 2^²⁵⁶. You have to create random data sets, convert them into hash, and then compare the two hashes. You have to do that for 2^²⁵⁶ times in worst case. If you have any idea how much that number is, you wouldn’t have had the security related doubt in the first place. For beginners, let’s begin by saying that the total number of atoms in the entire universe is 2^²⁶⁶. Doing little calculations (not so little), we get that if a supercomputer that can perform 15 trillion calculations per second is employed in cracking the hash, it would take almost years to crack the hash of a single Bitcoin address. Yeah, that sentence had two consecutive “billions”. 0.65 billion billion Now, according to , electronics (and hence computing) power will increase with time, and new advancements in the field of Quantum computers (Computers that works on the principles of quantum mechanics) would be able to beat the problem of reversing the hash. Moore’s law But even if a Quantum computer is employed, it would still take 10^ years to calculate one hash. The public key is passed through numerous one way hash functions which are essentially quantum-resistant. ³² That time period is longer than the 14 billion years the universe has existed, but less than the estimated 10^¹⁰⁰ years until the universe crunches during the heat death. Now, with the current heading, our computational capabilities doubles (Moore’s law states , but we will err on the side of caution). Even if it is so, only after 59 years, we would reach such computational capabilities by which we can crack and reverse one hash in . every year two years 1.3 years Ah-oh. Read on. Let’s get to some crazy physics facts about how long we can travel in this direction, tasked with the mathematical mission requiring us to solve a hash (The protector of Bitcoins). Enter my all time favorite storytelling tool. Physics. It is evident from the that a certain amount of energy is required to represent information. Shout out your name, write your name in your book, it requires energy transfer of some sort. Let’ say we are typing your name into the computer (or mobile). Certain transistors would need to switch states to represent and store that information. So, to change the system by even one bit, your system requires an energy no less than kT. second law of thermodynamics T happens to be the absolute temperature of the system and k is called the Boltzmann constant. The value of k is 1.38×10^(–16) erg/°Kelvin, and the ambient temperature of the universe approximates to 3.2°Kelvin. So our computers are operating at 3.2°Kelvin, given that we are not operating it somewhere outside the realms of classical physics, where laws of physics doesn’t work, . Let’s imagine that we are still on earth, doing this computation. Our ideal computer would consume 4.4×10^(–16) ergs every time we set or clear a bit. (Do something on your computer and all your activities like, click, drag, and key strokes, translates to transistor activities in the underlying circuits. The software in the midst handles the way humans interact with something as lifeless as a hardware system.) like inside the event horizon of a black hole Now, hold on with me on this ride. The annual energy of the sun is estimated to be at 1.21×10^ ⁴¹ ergs. This energy is enough to power almost 2.7×10^⁵⁶ single bit switching of our ideal computer. It is enough power to run a 187 bit counter through all its values. Imagine that we build a around the sun (Dyson sphere is an imaginary construct future civilizations are theorized to use to harvest the full power of sun by enwrapping the star with energy harvesters. These type of future human civilizations are called Type III civilizations. ). If we capture all of its energy continuously for 32 years without any sort of loss, we obtain enough power to operate a computer to count up to 2^¹⁹². After this upper limit, it won’t have power to calculate further more. Dyson sphere We are Type 1.5 You get the scale of energy we are talking about? Here are more, if you want to know how much it is. Be known that solar storms, small solar sparks that blows off the surface of the sun known as , are A single spark that may be flowing the way of earth one fine morning would cause an extinction level event (We missed one back in 2012, by the breadth of a hair, not ELE though). Coronal Mass ejections (CME) extinction level events(ELE). And here we are, discussing about harvesting sun’s total output for 32 years, and still it is unable to solve for a single SHA256 hash that protects the Bitcoin. So we can’t break the hash with sun’s energy. Why don’t we move over to higher order energy sources, such as a supernova explosions, which are the birthplaces of a star? The typical supernova gives off something like 10^⁵¹ ergs. If this energy could be channeled into solving for hashes, we would be able to count up to 219 bits. Still, our 256 bit is out of reach for such celestial machines such as stellar wombs. It has nothing to do with the technology. They are the upper limits thermodynamics will allow. If wasn’t the only way to crack well-crafted hashes, then the story would change. But fortunately, our only resort is start a brute force algorithm and hope that it would eventually run into the solution. brute force But it won’t. Breaking it would be infeasible until computers are made from things other than matter and occupy things other than space. The block chain technology was intelligently open-sourced so that when Quantum computers and Quantum algorithms such as Shor’s algorithms arrive, the keepers of the technology will advance the defenses to Quantum cryptography. But mind you, in case your account is hijacked or your private keys are compromised physically, then you are screwed. If the people suddenly start to abandon Bitcoin for something else, it would fall. Technologically it maybe incorruptible and un-hackable, but it is prone to the laws of economics. All these guarantees of the celestial machines won’t come to your salvation. Maybe government will impose strict rules out of fear, or maybe mass hackings of wallets will happen (because of your carelessness off course!!!). Maybe your private key gets stolen and it can lead to compromising your wallet. Block chain is the original technological backbone that empower Bitcoins. There are a lot of crypto currencies, like Litecoin, Ripple and Etherium, issued worldwide. All are empowered by block chain. There is a lot more to write about how block chain will revolutionize science, finance, education, politics and medicine. There are means by which this technology can dethrone world governments and all sorts of centralized authorizes and enforce a more efficient version of democracy. The implications are countless. But that’s a story for another time. ______________________ At WeHUBS Innovations, we always try to ponder the infinite with technologies like Artificial Intelligence, Augmented Reality and Computer Vision. Connect with us on . For collaborations and other enquiries , please visit . We would like to work with you on amazing ideas. Facebook wehubs.com

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