The fundamental equations of change in statistical ensembles and biological populations

TL;DR

This paper explores a unifying general equation for change in systems, linking thermodynamics, statistics, and biology, and demonstrating its equivalence to the Price equation in evolutionary theory.

Contribution

It introduces a unified mathematical framework for describing change across disciplines and shows its equivalence to the Price equation, enabling cross-disciplinary insights.

Findings

The general equation describes the dynamics of moments in probability distributions.

It establishes the equivalence between the general change equation and the Price equation.

The framework can unify diverse theories and derive new results in physics and biology.

Abstract

A recent article in Nature Physics unified key results from thermodynamics, statistics, and information theory. The unification arose from a general equation for the rate of change in the information content of a system. The general equation describes the change in the moments of an observable quantity over a probability distribution. One term in the equation describes the change in the probability distribution. The other term describes the change in the observable values for a given state. We show the equivalence of this general equation for moment dynamics with the widely known Price equation from evolutionary theory, named after George Price. We introduce the Price equation from its biological roots, review a mathematically abstract form of the equation, and discuss the potential for this equation to unify diverse mathematical theories from different disciplines. The new work in Nature Physics and many applications in biology show that this equation also provides the basis for deriving many novel theoretical results within each discipline.