General properties of nonlinear mean field Fokker-Planck equations

Details General properties of nonlinear mean field Fokker-Planck equations General properties of nonlinear mean field Fokker-Planck equations

2008-09-19

arxiv.org/abs/0809.3361v1

AIP Conf. Proc. 965, 144 (2007)

Physics

Condensed Matter

Statistical Mechanics

Paper presented at the international conference CTNEXT07, 1-5 july 2007, Catania, Italy

Scientific paper

10.1063/1.2828726

Recently, several authors have tried to extend the usual concepts of thermodynamics and kinetic theory in order to deal with distributions that can be non-Boltzmannian. For dissipative systems described by the canonical ensemble, this leads to the notion of nonlinear Fokker-Planck equation (T.D. Frank, Non Linear Fokker-Planck Equations, Springer, Berlin, 2005). In this paper, we review general properties of nonlinear mean field Fokker-Planck equations, consider the passage from the generalized Kramers to the generalized Smoluchowski equation in the strong friction limit, and provide explicit examples for Boltzmann, Tsallis and Fermi-Dirac entropies.

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