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arXiv · 0704.0465

A General Nonlinear Fokker-Planck Equation and its Associated Entropy

Veit Schwammle·Evaldo M. F. Curado·Fernando D. Nobre
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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.

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BibTeXRIS

Veit Schwammle, Evaldo M. F. Curado, Fernando D. Nobre. 2007-04-03. A General Nonlinear Fokker-Planck Equation and its Associated Entropy. https://doi.org/10.1140/epjb/e2007-00217-1

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