Consequences of the H-Theorem from Nonlinear Fokker-Planck Equations

Details Consequences of the H-Theorem from Nonlinear Fokker-Planck Equations Consequences of the H-Theorem from Nonlinear Fokker-Planck Equations

2007-07-20

arxiv.org/abs/0707.3153v1

Physics

Condensed Matter

Statistical Mechanics

19 pages, no figures

Scientific paper

10.1103/PhysRevE.76.041123

A general type of nonlinear Fokker-Planck equation is derived directly from a master equation, by introducing generalized transition rates. The H-theorem is demonstrated for systems that follow those classes of nonlinear Fokker-Planck equations, in the presence of an external potential. For that, a relation involving terms of Fokker-Planck equations and general entropic forms is proposed. It is shown that, at equilibrium, this relation is equivalent to the maximum-entropy principle. Families of Fokker-Planck equations may be related to a single type of entropy, and so, the correspondence between well-known entropic forms and their associated Fokker-Planck equations is explored. It is shown that the Boltzmann-Gibbs entropy, apart from its connection with the standard -- linear Fokker-Planck equation -- may be also related to a family of nonlinear Fokker-Planck equations.

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