Entropy and the arrow of time in population dynamics

TL;DR

This paper investigates entropy in population genetics models, especially the Moran process, exploring its implications for irreversibility, non-extensive entropies, and symmetries in evolutionary dynamics.

Contribution

It introduces an entropy formula for stochastic processes with multiple absorbing states and extends its analysis beyond the Moran process to other models.

Findings

Entropy relates to irreversibility in population dynamics.

Non-extensive entropies connect to epistasis effects.

Symmetries influence the behavior of genetic models.

Abstract

The concept of entropy in statistical physics is related to the existence of irreversible macroscopic processes. In this work, we explore a recently introduced entropy formula for a class of stochastic processes with more than one absorbing state that is extensively used in population genetics models. We will consider the Moran process as a paradigm for this class, and will extend our discussion to other models outside this class. We will also discuss the relation between non-extensive entropies in physics and epistasis (i.e., when the effects of different alleles are not independent) and the role of symmetries in population genetic models.