H-theorems for systems of coupled nonlinear Fokker-Planck equations

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 explor...

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Bibliographic Details
Published in:Europhysics letters 2022-07, Vol.139 (1), p.11002
Main Authors: Plastino, A. R., Wedemann, R. S., Nobre, F. D.
Format: Article
Language:English
Subjects:
Complex systems
Fokker-Planck equation
Free energy
Nonlinear dynamics
Nonlinear evolution equations
Nonlinear systems
Theorems
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Summary: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.
ISSN:0295-5075
1286-4854
DOI:10.1209/0295-5075/ac7c30