The European Physical Journal B

, Volume 58, Issue 2, pp 159–165

A general nonlinear Fokker-Planck equation and its associated entropy

Statistical and Nonlinear Physics

DOI: 10.1140/epjb/e2007-00217-1

Cite this article as:
Schwämmle, V., Curado, E. & Nobre, F. Eur. Phys. J. B (2007) 58: 159. doi:10.1140/epjb/e2007-00217-1


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.


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 

Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Authors and Affiliations

  1. 1.Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud 150, Rio de JaneiroRJBrazil