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

Abstract

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.