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The nonequilibrium potential today: A short review

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  • 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.

Suggested Citation

  • Wio, H.S. & Deza, J.I. & Sánchez, A.D. & García-García, R. & Gallego, R. & Revelli, J.A. & Deza, R.R., 2022. "The nonequilibrium potential today: A short review," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    • Handle: RePEc:eee:chsofr:v:165:y:2022:i:p1:s0960077922009572
    DOI: 10.1016/j.chaos.2022.112778
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    References listed on IDEAS

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    1. Izús, Gonzalo G. & Sánchez, Alejandro D. & Deza, Roberto R., 2009. "Noise-driven synchronization of a FitzHugh–Nagumo ring with phase-repulsive coupling: A perspective from the system’s nonequilibrium potential," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(6), pages 967-976.
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    1. Wang, Chuan & Xia, Hui, 2024. "Scaling properties and height distributions of persisting roughness in the discrete growth models in the presence of the angle of repose," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).

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