In the present paper, we have first studied the role of the maximum-entropy principle to explain the concept of organization of a physical system in the decreasing law of entropy with the increase of external constraints imposed on the system. We have then considered an open ecosystem (living) and determined a quantitative measure of ecological organization from the consideration of the thermodynamics of irreversible processes. Finally, we have tried to explain the evolution of the ecosystem in the light of Prigogine's principle of "order through fluctuation."
In this paper we first present a simple axiomatic derivation of Tsallis entropy as an extension of Shannon entropy. As an application we have first study the importance of Tsallis entropy in the statistical characterization of diversity of a population ecosystem. We next study some characteristic properties of an age-structured population on the basis of the Tsallis entropy.
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”
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