Multispecies effects in the equilibrium and out-of-equilibrium thermostatistics of overdamped motion

Abstract

Progress has been recently made, both theoretical and experimental, regarding the thermostatistics of complex systems of interacting particles or agents (species) obeying a nonlinear Fokker-Planck dynamics. However, major advances along these lines have been restricted to systems consisting of only one type of species. The aim of the present contribution is to overcome that limitation, going beyond single-species scenarios. We investigate the dynamics of overdamped motion in interacting and confined many-body systems having two or more species that experience different intra- A nd interspecific forces in a regime where forces arising from standard thermal noise can be neglected. Even though these forces are neglected, the behavior of the system can be analyzed in terms of an appropriate thermostatistical formalism. By recourse to a mean-field treatment, we derive a set of coupled nonlinear Fokker-Planck equations governing the behavior of these systems. We obtain an H theorem for this Fokker-Planck dynamics and discuss in detail an example admitting an exact, analytical stationary solution.