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 firstname.lastname@example.org
Published online: 10 August 2007
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.
PACS: 05.40.Fb – Random walks and Levy flights / 05.20.-y – Classical statistical mechanics / 05.40.Jc – Brownian motion / 66.10.Cb – Diffusion and thermal diffusion
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2007