Boltzmann, Darwin and Directionality theory
Abstract
Boltzmann’s statistical thermodynamics is a mathematical theory which relates the macroscopic properties of aggregates of interacting molecules with the laws of their interaction. The theory is based on the concept thermodynamic entropy, a statistical measure of the extent to which energy is spread throughout macroscopic matter. Macroscopic evolution of material aggregates is quantitatively explained in terms of the principle: Thermodynamic entropy increases as the composition of the aggregate changes under molecular collision. Darwin’s theory of evolution is a qualitative theory of the origin of species and the adaptation of populations to their environment. A central concept in the theory is fitness, a qualitative measure of the capacity of an organism to contribute to the ancestry of future generations. Macroscopic evolution of populations of living organisms can be qualitatively explained in terms of a neo-Darwinian principle: Fitness increases as the composition of the population changes under variation and natural selection. Directionality theory is a quantitative model of the Darwinian argument of evolution by variation and selection. This mathematical theory is based on the concept evolutionary entropy, a statistical measure which describes the rate at which an organism appropriates energy from the environment and reinvests this energy into survivorship and reproduction. According to directionality theory, microevolutionary dynamics, that is evolution by mutation and natural selection, can be quantitatively explained in terms of a directionality principle: Evolutionary entropy increases when the resources are diverse and of constant abundance; but decreases when the resource is singular and of variable abundance. This report reviews the analytical and empirical support for directionality theory, and invokes the microevolutionary dynamics of variation and selection to delineate the principles which govern macroevolutionary dynamics of speciation and extinction. We also elucidate the relation between thermodynamic entropy, which pertains to the extent of energy spreading and sharing within inanimate matter, and evolutionary entropy, which refers to the rate of energy appropriation from the environment and allocation within living systems. We show that the entropic principle of thermodynamics is the limit as R→0, M→∞, (where R denote the resource production rate, and M denote population size) of the entropic principle of evolution. We exploit this relation between the thermodynamic and evolutionary tenets to propose a physico-chemical model of the transition from inanimate matter which is under thermodynamic selection, to living systems which are subject to evolutionary selection.
Life history variation and the evolution of senescence The evolutionary dynamics of speciation and extinction Evolutionary trends in body size. The origin of sporadic forms of cancer and neurological diseases, and the evolution of cooperation are important recent applications of directionality theory. These applications, which draw from the medical sciences and sociobiology, appeal to methods which lie outside the formalism described in this report. A companion review, Demetrius and Gundlach (submitted for publication), gives an account of these applications.An important aspect of this report pertains to the connection between statistical mechanics and evolutionary theory and its implications towards understanding the processes which underlie the emergence of living systems from inanimate matter-a problem which has recently attracted considerable attention, Morowitz (1992), Eigen (1992), Dyson (2000), Pross (2012).The connection between the two disciplines can be addressed by appealing to certain extremal principles which are considered the mainstay of the respective theories.The extremal principle in statistical mechanics can be stated as follows:- Publication:
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Physics Reports
- Pub Date:
- September 2013
- DOI:
- 10.1016/j.physrep.2013.04.001
- Bibcode:
- 2013PhR...530....1D