## Abstract

The theory of evolution by natural selection is herein subsumed by the 2nd law of thermodynamics. The mathematical form of evolutionary theory is based on a re-examination of the probability concept that underlies statistical physics. Probability regarded as physical must include, in addition to isoenergic combinatorial configurations, also energy in conditional circumstances. Consequently, entropy as an additive logarithmic probability measure is found to be a function of the free energy, and the process toward the maximum entropy state is found equivalent to evolution toward the free energy minimum in accordance with the basic maxim of chemical thermodynamics. The principle of increasing entropy when given as an equation of motion reveals that expansion, proliferation, differentiation, diversification, and catalysis are all ways for a system to evolve toward the stationary state in its respective surroundings. Intriguingly, the equation of evolution cannot be solved when there remain degrees of freedom to consume the free energy, and hence evolutionary trajectories of a non-Hamiltonian system remain intractable. Finally, when to-and-from flows of energy are balanced between a system and its surroundings, the system is at the Lyapunov-stable stationary state. The principle of maximal energy dispersal, equivalent to the maximal rate of entropy production, gives rise to the ubiquitous characteristics, conventions, and regularities found in nature, where thermodynamics makes no demarcation line between animate and inanimate.

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