The nonequilibrium potential today: A short review

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

CHAOS, SOLITONS AND FRACTALS

PERGAMON-ELSEVIER SCIENCE LTD

Lugar: Amsterdam; Año: 2022 vol. 165 p. 112778 - 112789

0960-0779

A brief review is made of the birth and evolution of the ‘‘nonequilibrium potential’’ (NEP) concept. As ifproviding a landscape for qualitative reasoning were not helpful enough, the NEP adds a quantitative dimensionto the qualitative theory of differential equations and provides a global Lyapunov function for the deterministicdynamics. Here we illustrate the usefulness of the NEP to draw results on stochastic thermodynamics: theJarzynski 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 kineticinterface roughening). Additionally, we discuss system-size stochastic resonance in the Wilson–Cowan modeland relevant aspects of KPZ phenomenology like the EW–KPZ crossover and the memory of initial conditions.