Entropy production of cyclic population dynamics

TL;DR

This paper demonstrates that entropy production effectively characterizes nonequilibrium behaviors in cyclic population models, especially near critical transitions, providing analytical tools that align with simulations.

Contribution

It introduces a method to compute entropy production in nonequilibrium population dynamics and links it to critical behavior in cyclic competition models.

Findings

Entropy production peaks near the critical point of transition.

Analytical calculations match numerical simulations.

Entropy production approaches zero away from the critical point.

Abstract

Entropy serves as a central observable in equilibrium thermodynamics. However, many biological and ecological systems operate far from thermal equilibrium. Here we show that entropy production can characterize the behavior of such nonequilibrium systems. To this end we calculate the entropy production for a population model that displays nonequilibrium behavior resulting from cyclic competition. At a critical point the dynamics exhibits a transition from large, limit-cycle like oscillations to small, erratic oscillations. We show that the entropy production peaks very close to the critical point and tends to zero upon deviating from it. We further provide analytical methods for computing the entropy production which agree excellently with numerical simulations.