The nonequilibrium potential today: A short review

WIO, H.S.; DEZA, J.I.; SÁNCHEZ, A.D.; GARCÍA-GARCÍA, R.; GALLEGO, R.; REVELLI, J.A.; DEZA, R.R.

CHAOS, SOLITONS AND FRACTALS

PERGAMON-ELSEVIER SCIENCE LTD

Año: 2022 vol. 165

0960-0779

A brief review is made of the birth and evolution of the “nonequilibrium potential” (NEP) concept. As if providing a landscape for qualitative reasoning were not helpful enough, the NEP adds a quantitative dimension to the qualitative theory of differential equations and provides a global Lyapunov function for the deterministic dynamics. Here we illustrate the usefulness of the NEP to draw results on stochastic thermodynamics: the Jarzynski equality in the Wilson–Cowan model (a population-competition model of the neocortex) and a “thermodynamic uncertainty relation” (TUR) in the KPZ equation (the stochastic field theory of kinetic interface roughening). Additionally, we discuss system-size stochastic resonance in the Wilson–Cowan model and relevant aspects of KPZ phenomenology like the EW–KPZ crossover and the memory of initial conditions.