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.

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.

• Journal Article Type: Article
• Acceptance Date: Oct 2, 2022
• Online Publication Date: Oct 20, 2022
• Publication Date: Dec 1, 2022
• Deposit Date: Oct 21, 2022
• Publicly Available Date: Oct 21, 2024
• Journal: Chaos, Solitons and Fractals
• Print ISSN: 0960-0779
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 165
• Issue: Part 1
• Pages: 112778
• DOI: https://doi.org/10.1016/j.chaos.2022.112778
• Keywords: General Mathematics; General Physics and Astronomy; Statistical and Nonlinear Physics; Applied Mathematics, Nonequilibrium potential Stochastic thermodynamics KPZ equation
• Public URL: https://uwe-repository.worktribe.com/output/10100827
• Publisher URL: https://authors.elsevier.com/c/1fxuy3QI~FVu7a
• Additional Information: This article is maintained by: Elsevier; Article Title: The nonequilibrium potential today: A short review; Journal Title: Chaos, Solitons & Fractals; CrossRef DOI link to publisher maintained version: https://doi.org/10.1016/j.chaos.2022.112778; Content Type: article; Copyright: © 2022 Elsevier Ltd. All rights reserved.; ; H.S.W. and R.R.D. thank warmly M. A. Rodríguez and R. Toral for enlightening discussions on the subject of this work, sustained along more than three decades. A.D.S. and R.R.D. acknowledge support by UNMdP, Argentina through project EXA1033/21–15/E991.