The nonequilibrium potential today: A short review. (December 2022)

• Record Type: Journal Article
• Authors: Wio, H.S.; Deza, J.I.; Sánchez, A.D.; García-García, R.; Gallego, R.; Revelli, J.A.; Deza, R.R.
• Is Part Of: Chaos, solitons and fractals. Volume 165:Part 1(2022)
• Publication Date: 2022-12
• Subjects: Nonequilibrium potential -- Stochastic thermodynamics -- KPZ equation; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2022.112778
• Languages: English
• ISSNs: 0960-0779

Abstract

Abstract: 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. Highlights: A brief review is made of the birth and evolution of the "nonequilibrium potential" concept, including relevant bibliography on some now "classical" systems admitting a NEP: the complex Ginzburg–Landau equation (CGLE) and the FitzHugh–Nagumo (FHN) model. Other system introduced is: The KPZ equation—a stochastic field theory of kinetic interface roughening—is shown to be a gradient system: the functional it stems from displays the Lyapunov property, but unbound from below conserving memory of the process, yielding a visual criterion for the EW–KPZ crossover. The Wilson–Cowan model of the neocortex—describing the competition between excitatory and inhibitory neural populations—is generically a system admitting a bona-fide NEP. The usefulness of the NEP concept to draw results on stochastic thermodynamics is illustrated through a Jarzynski equality in the Wilson–Cowan model and a thermodynamic uncertainty relation (TUR) in the KPZ equation. Furher illustrations of the usefulness of the NEP concept are the memory of initial conditions in KPZ and system-size stochastic resonance in the Wilson–Cowan model.