  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.

Statistical Mechanics