Biological Evolution: Entropy, Complexity and Stability
ABSTRACT
In the present paper we have made an attempt to investigate the importance of the concepts of dynamical stability and complexity along with their interelationship in an evolving biological systems described by a system of kinetic (both deterministic and chaotic) equations. The key to the investigation lies in the expres-sion of a time-dependent Boltzmann-like entropy function derived from the dynamical model of the system. A significant result is the determination of the expression of Boltzmann - entropy production rate of the evolving system leading to the well-known Pesin-type identity which provides an elegant and simple meas-ure of dynamical complexity in terms of positive Lyapunov exponents. The expression of dynamical com-plexity has been found to be very suitable in the study of the increase of dynamical complexity with the suc-cessive instabilities resulting from the appearance of new polymer species (or ecological species) into the original system. The increase of the dynamical complexity with the evolutionary process has been explained with a simple competitive model system leading to the “principle of natural selection”.
In the present paper we have made an attempt to investigate the importance of the concepts of dynamical stability and complexity along with their interelationship in an evolving biological systems described by a system of kinetic (both deterministic and chaotic) equations. The key to the investigation lies in the expres-sion of a time-dependent Boltzmann-like entropy function derived from the dynamical model of the system. A significant result is the determination of the expression of Boltzmann - entropy production rate of the evolving system leading to the well-known Pesin-type identity which provides an elegant and simple meas-ure of dynamical complexity in terms of positive Lyapunov exponents. The expression of dynamical com-plexity has been found to be very suitable in the study of the increase of dynamical complexity with the suc-cessive instabilities resulting from the appearance of new polymer species (or ecological species) into the original system. The increase of the dynamical complexity with the evolutionary process has been explained with a simple competitive model system leading to the “principle of natural selection”.
KEYWORDS
Boltzmann-Entropy, Dynamical Stability, Pesin-type Identity and Dynamical Complexity, Lyapunov Exponents, Structural Instabilities, Biological Evolution
Boltzmann-Entropy, Dynamical Stability, Pesin-type Identity and Dynamical Complexity, Lyapunov Exponents, Structural Instabilities, Biological Evolution
Cite this paper
nullC. Chakrabarti and K. Ghosh, "Biological Evolution: Entropy, Complexity and Stability," Journal of Modern Physics, Vol. 2 No. 6, 2011, pp. 621-626. doi: 10.4236/jmp.2011.226072.
nullC. Chakrabarti and K. Ghosh, "Biological Evolution: Entropy, Complexity and Stability," Journal of Modern Physics, Vol. 2 No. 6, 2011, pp. 621-626. doi: 10.4236/jmp.2011.226072.
References
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[1] G. Nicolis and I. Prigogine : Self- Organization in Non-Equilibrium Systems. Wiley and Sons, New York, 1977. [2] I. Prigogine and G. Nicolis : Biological Order, Structure and Instability. Quart. Rev. Biophys, 4, 107, 1971. [3] I. Prigogine, G. Nicolis and A. Babloyantz : Thermodynamics of Evolution. Part-1. Phys. Today, 25, 23, 1972; Part-2, Phys. Today, 25, 38, 1972. [4] L. Demetrius: Thermodynamics and Evolution. J. Theoret. Biol., 206, 1, 2000. [5] B. H. Weber, D. J. Depew, J. D. Smith (eds): Entropy, Information and Evolution, Cambridge, M.I.T Press, 2000. [6] R. Feistel and W. Ebeling: Evolution of Complex System, Kluwer Academic Pulb., Dordrecht, 1989. [7] W. Ebeling and R. Feistel: Theory of Self-Organization and Evolution. The Role of Entropy, Value and Information. J. Non-Equil. Thermod., 17, 303, 1992. [8] T. S. Ray: Evolution, Complexity and Artificial Reality. Physica D, 75, 239-263, 1994. [9] B. Drossel: Biological Evolution and Statistical Physics. Advances in Physics, 50, 209, 2001. [10] N. H. Barton and J. Coe: In the Application of Statistical Physics to Evolutionary Biology. J. Theoret. Biol. 259, 317, 2009. [11] C.G. Chakrabarti and S.Ghosh: (a) Statistical Mechanics of Complex System. Ind. J. Theort. Phys. 48, 43, 1995. (b) Entropic Models and Analysis of Complex Systems.SAMS,23,103,1996. [12] C. G. Chakrabarti and Koyel Ghosh: Maximum-Entropy Principle: Ecological organization and Evolution.J. Biol. Phys. vol. 36, issue 2, 175, DOI 10.1007/s 10867-009-9170-z. 2010. [13] S. Loyld and H. Pagels: Complexity and Thermodynamic Depth. Ann. Phys., 188, 186, 1988. [14] G. Jumarie: Maximum Entropy, Information without Probability and Complex Fractals. Kluwer Academic Publishers, Dordrecht, 2000. [15] S. H. Strogatz: Non-Linear Dynamics and Chaos. Addison-Weslay Pbl.co. New-York, 1994. [16] K. T. Aligood, T. D. Sauer and J. A. Yorke: Chaos: An Introduction to Dynamical System.,Springer, New-York, 1997. [17] R. C. Hilborn: Chaos and Non-Linear Dynamics. Oxford Univ. Press. Oxford, 2000. [18] J. R. Dorfman: An Introduction to Chaos and Non-Equilibrium Statistical Mechanics. Cambridge Univ. Press, Cambridge, 1999. [19] N. Korabel and Eli Barkai: Pesin Type Identity for Intermittent Dynamics with Zero Lyapunov Exponent. Phys. Rev. Lett., 102, 050601, 2009. [20] V. S. Anishchenko et al: Non-Linear Dynamics of Chaotic and Stochastic Systems. Springer, New-York, 2001. [21] V. Latora and M. Baranger. K. S. Entropy Rate Vs Physical Entropy. Phys. Rev. Lett.,82, 520, 1999. [22] C. Beck and F. Sc l gl: Thermodynamics of Chaotic Systems. Cambridge Univ. Press, Cambridge, 1997. [23] H. Haken: Advanced Synergetics. Springer, New-York, 1983. [24] C. G. Chakrabarti, S. Ghosh, and S. Bhadra: Non-equilibrium Thermodynamics of Lotka-Volterrra Ecosystem: Stability and Evolution. J. Biol. Phys.21, 273 (1995). [25] R. V. Sole' and J. Bascompte: Self-Organization in Complex Ecosystems. Princeton Univ. Press, Princeton, 2004.