General properties of nonlinear mean field Fokker-Planck equations
Statistical Mechanics
2009-11-13 v1
Abstract
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.
Keywords
Cite
@article{arxiv.0809.3361,
title = {General properties of nonlinear mean field Fokker-Planck equations},
author = {Pierre-Henri Chavanis},
journal= {arXiv preprint arXiv:0809.3361},
year = {2009}
}
Comments
Paper presented at the international conference CTNEXT07, 1-5 july 2007, Catania, Italy