Entropy and the arrow of time in population dynamics. (January 2023) - Costa-Cabanas, Diogo; Chalub, Fabio A.C.C.; Souza, Max O.
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. Highlights: We use statistical mechanics techniques to study population dynamics. Biological evolution is modelled by agent interaction (microscopic laws). We are concerned by macroscopic variables (population state). We explore a recently introduced formula for entropy for processes with absorption. We discuss why population dynamics exhibit macroscopic irreversibility.