Systems consisting of confined, interacting particles doing overdamped motion admit an effective description in terms of nonlinear Fokker–Planck equations. The behavior of these systems is closely related to the power-law entropies and can be interpreted in terms of the -based thermostatistics. The connection between overdamped systems and the measures provides valuable insights on diverse physical problems, such as the dynamics of interacting vortices in type-II superconductors. The -thermostatistical approach to the study of many-body systems described by nonlinear Fokker–Planck equations has been intensively explored in recent years, but most of these efforts were restricted to systems affected by time-independent external potentials. Here, we extend this treatment to systems evolving under time-dependent external forces. We establish a lower bound on the work done by these forces when they drive the system during a transformation. The bound is expressed in terms of a free energy based on the entropy and is satisfied even if the driving forces are not derivable from a potential function. It constitutes a generalization, for systems governed by nonlinear Fokker–Planck equations involving general time-dependent external forces, of the -theorem satisfied by these systems when the external forces arise from a time-independent potential.
Statistical dynamics of driven systems of confined interacting particles in the overdamped-motion regime
Note: This article is part of the Focus Issue on Complex Systems and Inter/Transdisciplinary Research.
S. Curilef, A. R. Plastino, R. S. Wedemann; Statistical dynamics of driven systems of confined interacting particles in the overdamped-motion regime. Chaos 1 November 2022; 32 (11): 113134. https://doi.org/10.1063/5.0104907
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