A General Nonlinear Fokker-Planck Equation and its Associated Entropy

Details A General Nonlinear Fokker-Planck Equation and its Associated Entropy A General Nonlinear Fokker-Planck Equation and its Associated Entropy

2007-04-03

arxiv.org/abs/0704.0465v1

Physics

Condensed Matter

Statistical Mechanics

17 pages, submitted to Eur. Phys. J. B

Scientific paper

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.

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