Eur. Phys. J. B 58, 159-165 (2007)
https://doi.org/10.1140/epjb/e2007-00217-1

A general nonlinear Fokker-Planck equation and its associated entropy

Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud 150, Rio de Janeiro, RJ, 22290-180, Brazil

Corresponding author: ^a fdnobre@cbpf.br

Received: 3 April 2007
Published online: 10 August 2007

Abstract

A recently introduced nonlinear Fokker-Planck equation, derived directly from a master equation, comes out as a very general tool to describe phenomenologically systems presenting complex behavior, like anomalous diffusion, in the presence of external forces. Such an equation is characterized by a nonlinear diffusion term that may present, in general, two distinct powers of the probability distribution. Herein, we calculate the stationary-state distributions of this equation in some special cases, and introduce associated classes of generalized entropies in order to satisfy the H-theorem. Within this approach, the parameters associated with the transition rates of the original master-equation are related to such generalized entropies, and are shown to obey some restrictions. Some particular cases are discussed.