Action, an Extensive Property of Self – Organizing Systems
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Abstract
The Principle of Least Action has evolved and established itself as the most basic law of physics. This allows us to see how this fundamental law of nature determines the development of the system towards states with less action, i.e., organized states. The intrinsic properties of complex systems are investigated. A system undergoing a natural process is formulated as a game that tends to organize the system in the least possible time. Nash – equilibrium strategy profile is being proposed as an attractor for self – organizing complex systems.
References
[1] Ville, R., Kaila, I. and Annila, A., “Natural selection for least action” Proceedings of The Royal Society 464, 3055-3070 (2008).
[2] Georgiev, G. and Georgiev, I., “The Least Action and the Metric of an Organized system” open systems and information dynamics 9, (4) 371-380 (2002).
[3] Neumann, J. von & Morgenstern, O., Theory of Games and Economic Behavior, Princeton University Press, (1944).
[4] Nash, J. F., Jr., “Equilibrium points in N-person games”, Proceedings of National Academy of Sciences 36, 48-49 (1950).
[5] Nash, J. F., Jr., Non-cooperative Games, PhD Thesis.
View more references (31)
[6] Anttila, J., Annila, A., “Natural games”, Physics Letters A, (In press), doi: 10.1016/ j.physleta.2011.08.056 (2011).
[7] Bejan, Adrian, Advanced Engineering Thermodynamics, John Wiley, (1998).
[8] Cengel, Y. A. and Boles, M. A., Thermodynamics: An Engineering Approach, McGraw Hill, (1988).
[9] Prigogine, I., Introduction to the Thermodynamics of Irreversible Processes, Wiley, (1961).
[10] Maupertuis, Pierre de, Essai de cosmologie, (1750).
[11] Peterson, S., “The geometry of virtual work dynamics in screw space, “Journal of applied mechanics-transactions of the ASME, 59, (2) 411 (1992).
[12] Papastavridis, J. G., “The principle of least action as a lagrange variational problem - stationarity and extremality conditions,” Int J Eng Sci 24, (8) 1437 (1986).
[13] Goldstein, H., Classical Mechanics, 2nd ed., Addison Wesley, (1980).
[14] Kauffman, S., The Origins of Order: Self-organization and selection in evolution, Oxford, (1993).
[15] Lewin, R., Complexity: life at the edge of chaos, Macmillan, (1992).
[16] Bak, P., How Nature Works: The science of self-organized criticality, Copernicus, Springer Verlag, (1996).
[17] Coveney, P. & Highfield, R., Frontiers of Complexity: The search for order in a chaotic world, Fawcett Columbine, (1995).
[18] Salthe, S. N., Development and Evolution, MIT Press, (1993).
[19] Bar-Yam, Y., Dynamics of Complex Systems, Addison Wesley, (1997).
[20] Feynman, R. P., “Space–time approach to non-relativistic quantum mechanics”, Rev. Mod. Phys. 20, 367–387 (1948)
[21] Feynman, R. P. & Hibbs, A. R., Quantum mechanics and path integrals, McGraw-Hill, (1965).
[22] Gyarmati, I., Nonequilibrium thermodynamics: field theory and variational principles, Springer, (1970).
[23] Hanc, J. & Taylor, E. F., “From conservation of energy to the principle of least action: a story line” Am. J. Phys. 72, 514–521 (2004).
[24] Hanc, J., Taylor, E. F. & Tuleja, S., „Deriving Lagrange‟s equations using elementary calculus”, Am. J. Phys. 72, 510–513(2004).
[25] Lotka, A. J., “Natural selection as a physical principle” Proc. Natl Acad. Sci. 8, 151 -154 (1922)
[26] Schro¨dinger, E., What is life? The physical aspects of the living cell, Cambridge University Press, (1948)
[27] Zambrini, J. C., “Maupertuis principle of least action in stochastic calculus of variations,” J math phys 25, (5) 1314 (1984).
[28] Broucke, R., “On the principle of least action - some possible generalizations,” Hadronic J. 5, (5) 1901 (1982).
[29] Nadj, H., Nadj, J. & Nadj, M., “Relativity as consequence of the principle of least action,” Am phys soc 26, (3) 472 (1981).
[30] Chaisson, E. J., The cosmic Evolution, Harvard, (2001).
[31] Chaisson, E. J., “The cosmic environment for the growth of complexity,” BioSystems, 46, 13 (1998).
[32] Goerner, S. J., Chaos and the evolving ecological Universe, Gordon and Breach, (1994).
[33] Collier, J. D. & Hooker, C. A., “Complexly Organised Dynamical Systems,” Open Systems & InformationDynamics 6, 241 (1999).
[34] Laszlo, E., Evolution: the grand synthesis, Shambhala, (1987)
[35] Jantsch, E., The Self-Organizing Universe, Pergamon, Oxford, (1980).
[36] Arfken, G. B. & Weber, H. J., Mathematical Methods for Physicists, 4th ed., Academic Press, (1995).