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 165, 112778 (11pgs) (2022)

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.

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