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Abstract: Recently, several authors have tried to extend the usual concepts ofthermodynamics and kinetic theory in order to deal with distributions that canbe non-Boltzmannian. For dissipative systems described by the canonicalensemble, this leads to the notion of nonlinear Fokker-Planck equation T.D.Frank, Non Linear Fokker-Planck Equations, Springer, Berlin, 2005. In thispaper, we review general properties of nonlinear mean field Fokker-Planckequations, consider the passage from the generalized Kramers to the generalizedSmoluchowski equation in the strong friction limit, and provide explicitexamples for Boltzmann, Tsallis and Fermi-Dirac entropies.



Autor: Pierre-Henri Chavanis

Fuente: https://arxiv.org/







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