Issue |
EPL
Volume 139, Number 1, July 2022
|
|
---|---|---|
Article Number | 11002 | |
Number of page(s) | 6 | |
Section | Statistical physics and networks | |
DOI | https://doi.org/10.1209/0295-5075/ac7c30 | |
Published online | 20 July 2022 |
H-theorems for systems of coupled nonlinear Fokker-Planck equations
1 CeBio y Departamento de Ciencias Básicas, Universidad Nacional del Noroeste de la Província de Buenos Aires (UNNOBA), CONICET - Roque Saenz Peña 456, Junin, Argentina
2 Instituto de Matemática e Estatística, Universidade do Estado do Rio de Janeiro (UERJ) Rua São Francisco Xavier 524, 20550-900, Rio de Janeiro, RJ, Brazil
3 Centro Brasileiro de Pesquisas Físicas (CBPF) and National Institute of Science and Technology for Complex Systems - Rua Xavier Sigaud 150, 22290-180, Rio de Janeiro - RJ, Brazil
(a) arplastino@unnoba.edu.ar (corresponding author)
(b) roseli@ime.uerj.br
(c) fdnobre@cbpf.br
Received: 18 February 2022
Accepted: 27 June 2022
Nonlinear diffusion and Fokker-Planck equations constitute valuable tools in the study of diverse phenomena in complex systems. Processes described by these equations are closely related to thermostatistical formalisms based on generalized entropic functionals. Inspired by these relations, we explore the behavior of systems of coupled, nonlinear Fokker-Planck equations. In particular, we establish an H-theorem for a wide family of this type of systems. This H-theorem is formulated in terms of an appropriate free-energy–like functional. The nonlinear evolution equations discussed here include, as particular instances, those governing the dynamics of interacting multi-species, many-body systems in the overdamped-motion regime.
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