Statistical Physics of Evolving Systems
Abstract
:1. Introduction
2. Materials and Methods
2.1. The State Equation
2.2. The Evolutionary Equation
2.3. The Continuous Equation of Motion
3. Results
3.1. The Ubiquitous Patterns
3.2. Non-Deterministic Motion
4. Discussion
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
- Boltzmann, L. The Second Law of Thermodynamics; D. Reidel: Dordrecht, Holland, 1974. [Google Scholar]
- Demetrius, L. Thermodynamics and Evolution. J. Theor. Biol. 2000, 206, 1–16. [Google Scholar] [CrossRef] [Green Version]
- Annila, A.; Salthe, S. Physical foundations of evolutionary theory. J. Non-Equil. Therm. 2010, 35, 301–321. [Google Scholar] [CrossRef]
- Roach, T.N.F. Use and Abuse of Entropy in Biology: A Case for Caliber. Entropy 2020, 22, 1335. [Google Scholar] [CrossRef]
- Styer, D. Entropy as Disorder: History of a Misconception. Phys. Teach. 2019, 57, 454–458. [Google Scholar] [CrossRef] [Green Version]
- Schrödinger, E. What is Life—The Physical Aspect of the Living Cell; Cambridge University Press: Cambridge, UK, 1944. [Google Scholar]
- Boltzmann, L. Populäre Schriften; Barth: Leipzig, Germany, 1905. [Google Scholar]
- Loschmidt, J. Uber den Zustand des Warmegleichgewichtes eines Systems von Korpern mit Rücksicht auf die Schwerkraft. Wien. Ber. 1876, 73, 28–142. [Google Scholar]
- Zermelo, E. On the mechanical explanation of irreversible processes. Ann. Phys. 1896, 59, 793–801. [Google Scholar] [CrossRef] [Green Version]
- Lucia, U. Second law considerations on the third law: From Boltzmann and Loschmidt paradox to non equilibrium temperature. Phys. A Stat. Mech. Its Appl. 2016, 444, 121–128. [Google Scholar] [CrossRef]
- Vilar, J.M.G.; Rubí, J.M. Thermodynamics “beyond” local equilibrium. Proc. Natl. Acad. Sci. USA 2001, 98, 11081–11084. [Google Scholar] [CrossRef] [Green Version]
- Kondepudi, D.K.; Prigogine, I. Modern Thermodynamics: From Heat Engines to Dissipative Structures; John Wiley & Sons: Hoboken, NJ, USA, 1999. [Google Scholar]
- Onsager, L. Reciprocal Relations in Irreversible Processes. I. Phys. Rev. 1931, 37, 405–426. [Google Scholar] [CrossRef]
- Edwards, A.W.F. Mathematizing Darwin. Behav. Ecol. Sociobiol. 2011, 65, 421–430. [Google Scholar] [CrossRef] [Green Version]
- De Groot, S.R.; Mazur, P. Non-Equilibrium Thermodynamics; Dover Publications: New York, NY, USA, 2013. [Google Scholar]
- Popper, K.R. The Logic of Scientific Discovery; Routledge: New York, NY, USA, 2002. [Google Scholar]
- Schmidt-Nielsen, K. Scaling: Why is Animal Size So Important? Cambridge University Press: Cambridge, UK, 1984; p. 241. [Google Scholar]
- Snell, O. Die Abhängigkeit des Hirngewichts von dem Körpergewicht und den geistigen Fähigkeiten. Arch. Psychiatr. 1892, 23, 436–446. [Google Scholar] [CrossRef] [Green Version]
- Thompson, D.A.W. On Growth and Form; Cambridge University Press: Cambridge, UK, 1992. [Google Scholar]
- Huxley, J.S. Problems of Relative Growth, 2nd ed.; Dover: New York, NY, USA, 1972. [Google Scholar]
- Pinto, C.M.A.; Mendes Lopes, A.; Machado, J.A.T. A review of power laws in real life phenomena. Commun. Nonlinear Sci. Numer. Simul. 2012, 17, 3558–3578. [Google Scholar] [CrossRef] [Green Version]
- West, G. Scale: The Universal Laws of Life, Growth, and Death in Organisms, Cities, and Companies; Penguin Publishing Group: New York, NY, USA, 2017. [Google Scholar]
- West, G.B.; Brown, J.H.; Enquist, B.J. A general model for the origin of allometric scaling laws in biology. Science 1997, 276, 122–126. [Google Scholar] [CrossRef]
- Demetrius, L. Quantum statistics and allometric scaling of organisms. Phys. A Stat. Mech. Its Appl. 2003, 322, 477–490. [Google Scholar] [CrossRef]
- Newman, M.E.J. Power laws, Pareto distributions and Zipf’s law. Contemp. Phys. 2005, 46, 323–351. [Google Scholar] [CrossRef] [Green Version]
- Limpert, E.; Stahel, W.; Abbt, M. Lognormal Distributions Across the Sciences: Keys and Clues. Bioscience 2001, 51, 341–352. [Google Scholar] [CrossRef]
- Annila, A.; Kuismanen, E. Natural hierarchy emerges from energy dispersal. Biosystems 2009, 95, 227–233. [Google Scholar] [CrossRef] [Green Version]
- Newton, I. Opticks: Or, a Treatise of the Reflexions, Refractions, Inflexions and Colours of Light, 4th ed.; William Innys: St. Paul’s, MN, USA, 1703; p. 382. [Google Scholar]
- Lewis, G.N. The Conservation of Photons. Nature 1926, 118, 874–875. [Google Scholar] [CrossRef]
- Annila, A. All in Action. Entropy 2010, 12, 2333–2358. [Google Scholar] [CrossRef] [Green Version]
- Grahn, P.; Annila, A.; Kolehmainen, E. On the carrier of inertia. AIP Adv. 2018, 8, 035028. [Google Scholar] [CrossRef] [Green Version]
- Wilson, C.M.; Johansson, G.; Pourkabirian, A.; Simoen, M.; Johansson, J.R.; Duty, T.; Nori, F.; Delsing, P. Observation of the Dynamical Casimir Effect in a Superconducting Circuit. Nature 2011, 479, 376. [Google Scholar] [CrossRef]
- Einstein, A.; Podolsky, B.; Rosen, N. Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. Lett. 1935, 47, 777–780. [Google Scholar] [CrossRef] [Green Version]
- Sharma, V.; Annila, A. Natural process—Natural selection. Biophys. Chem. 2007, 127, 123–128. [Google Scholar] [CrossRef] [PubMed] [Green Version]
- Annila, A. Natural thermodynamics. Phys. A 2016, 444, 843–852. [Google Scholar] [CrossRef]
- Michaelian, K.; Santamaria-Holek, I. Invalid Microstate Densities for Model Systems Lead to Apparent Violation of Thermodynamic Law. Entropy 2017, 19, 314. [Google Scholar] [CrossRef] [Green Version]
- Gibbs, J.W. Elementary Principles in Statistical Mechanics: Developed with Especial Reference to the Rational Foundation of Thermodynamics; Charles Scribner’s Sons: New York, NY, USA, 1902. [Google Scholar] [CrossRef]
- Falcon, A. Aristotle on Causality. In The Stanford Encyclopedia of Philosophy, Spring 2021 ed.; Zalta, E.N., Ed.; Metaphysics Research Lab, Stanford University: Stanford, CA, USA, 2019. [Google Scholar]
- Michaelian, K. Microscopic dissipative structuring and proliferation at the origin of life. Heliyon 2017, 3, e00424. [Google Scholar] [CrossRef]
- Michaelian, K. The Dissipative Photochemical Origin of Life: UVC Abiogenesis of Adenine. Entropy 2021, 23, 217. [Google Scholar] [CrossRef] [PubMed]
- Annila, A.; Annila, E. Why did life emerge? Int. J. Astrobiol. 2008, 7, 293–300. [Google Scholar] [CrossRef]
- Karnani, M.; Annila, A. Gaia again. Biosystems 2009, 95, 82–87. [Google Scholar] [CrossRef]
- Jaakkola, S.; Sharma, V.; Annila, A. Cause of Chirality Consensus. Curr. Chem. Biol. 2008, 2, 153–158. [Google Scholar] [CrossRef]
- Würtz, P.; Annila, A. Roots of diversity relations. J. Biophys. 2008, 2008, 654672. [Google Scholar] [CrossRef] [PubMed] [Green Version]
- De Maupertuis, P.-L.M. Les loix du mouvement et du repos déduites d’un principe métaphysique. Hist. l’Académie R. Sci. Belles Lett. 1748, 1746, 267–294. [Google Scholar]
- Chatterjee, A. Thermodynamics of Action and Organization in a System. Complexity 2016, 21, 307–317. [Google Scholar] [CrossRef]
- Kuchling, F.; Friston, K.; Georgiev, G.; Levin, M. Morphogenesis as Bayesian inference: A variational approach to pattern formation and control in complex biological systems. Phys. Life Rev. 2020, 33, 88–108. [Google Scholar] [CrossRef]
- Riek, R.; Chatterjee, A. Causality in Discrete Time Physics Derived from Maupertuis Reduced Action Principle. Entropy 2021, 23, 1212. [Google Scholar] [CrossRef]
- Chatterjee, A.; Iannacchione, G. Time and thermodynamics extended discussion on “Time & clocks: A thermodynamic approach”. Results Phys. 2020, 17, 103165. [Google Scholar] [CrossRef]
- Simon, H.A. On a Class of Skew Distribution Functions. Biometrika 1955, 42, 425–440. [Google Scholar] [CrossRef]
- Mäkelä, T.; Annila, A. Natural patterns of energy dispersal. Phys. Life Rev. 2010, 7, 477–498. [Google Scholar] [CrossRef]
- Georgiev, G.Y.; Chatterjee, A.; Iannacchione, G. Exponential Self-Organization and Moore’s Law: Measures and Mechanisms. Complexity 2017, 2017, 1–9. [Google Scholar] [CrossRef]
- May, R.M. Simple mathematical models with very complicated dynamics. Nature 1976, 261, 459–467. [Google Scholar] [CrossRef]
- Aitchison, J.; Brown, J.A.C. The Lognormal Distribution with Special Reference to Its Uses in Economics; Cambridge University Press: Cambridge, UK, 1963. [Google Scholar]
- Gaddum, J.H. Lognormal Distributions. Nature 1945, 156, 463–466. [Google Scholar] [CrossRef]
- Tsuji, K.; Müller, S.C. Spirals and Vortices: In Culture, Nature, and Science; Springer International Publishing: Berlin/Heidelberg, Germany, 2019. [Google Scholar]
- Annila, A. Physical portrayal of computational complexity. ISRN Comp. Math. 2012, 321372, 15. [Google Scholar] [CrossRef] [Green Version]
- Lucia, U.; Grisolia, G. Irreversible Thermodynamics and Bioeconomy: Toward a Human-Oriented Sustainability. FrPhy 2021, 9, 154. [Google Scholar] [CrossRef]
- Kuhn, T.S. The Essential Tension: Selected Studies in Scientific Tradition and Change; Chicago University Press: Chicago, IL, USA, 1977; p. 366. [Google Scholar]
- Strogatz, S.H. Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering; CRC Press: New York, NY, USA, 2018. [Google Scholar]
- Bacon, F. Novum Organum; Cambridge University Press: Cambridge, UK, 2000; p. 252. [Google Scholar]
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Annila, A. Statistical Physics of Evolving Systems. Entropy 2021, 23, 1590. https://doi.org/10.3390/e23121590
Annila A. Statistical Physics of Evolving Systems. Entropy. 2021; 23(12):1590. https://doi.org/10.3390/e23121590
Chicago/Turabian StyleAnnila, Arto. 2021. "Statistical Physics of Evolving Systems" Entropy 23, no. 12: 1590. https://doi.org/10.3390/e23121590
APA StyleAnnila, A. (2021). Statistical Physics of Evolving Systems. Entropy, 23(12), 1590. https://doi.org/10.3390/e23121590