The nonequilibrium potential today: A short review

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.