Entropy production of cyclic population dynamics

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.

4 pages, 3 figures and Supplementary Material. To appear in Phys. Rev. Lett..

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• Mobility promotes and jeopardizes biodiversity in rock-paper-scissors games
• Coevolutionary dynamics in large, but finite populations
• Zero-one survival behavior of cyclically competing species
• Intrinsic noise in game dynamical learning
• Anomalous finite-size effects in the Battle of the Sexes

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