Directionality theory and the second law of thermodynamics

Abstract

The statistical mechanics of molecular collisions in a macroscopic body is encoded by the parameter Thermodynamic entropy — a statistical measure of the number of molecular configurations that correspond to a given macrostate. Irreversibility in the flow of energy in macroscopic bodies is determined by random molecular interactions and expressed by the Second Law of Thermodynamics: In isolated systems, that is systems closed to the input of energy and matter, thermodynamic entropy increases.The evolutionary dynamics of a population of replicating organisms is encoded by the parameter Evolutionary entropy, a statistical measure of the number and diversity of metabolic cycles generated by the replication and viability of the individual organisms. Irreversibility in the transformation of energy in populations of organisms is determined by random mutation and natural selection. Changes in the organization of metabolic energy are described by the Directionality Principle of Evolution: Evolutionary entropy increases, when the energy source is limited and constant and decreases when the energy source is abundant and inconstant.This article shows that, when R→0, and N→∞ (where R denotes the production rate of the external energy source; N the number of replicating organisms) evolutionary entropy, a measure of spatio-temporal organization, and thermodynamic entropy, a measure of positional disorder, coincide. We invoke this relation between thermodynamic and evolutionary entropy to show that the Directionality Principle for Evolution is a generalization of the Second Law of Thermodynamics.