Generalized Fokker-Planck equations and effective thermodynamics
Statistical Mechanics
2009-11-11 v1
Abstract
We introduce a new class of Fokker-Planck equations associated with an effective generalized thermodynamical framework. These equations describe a gas of Langevin particles in interaction. The free energy can take various forms which can account for anomalous diffusion, quantum statistics, lattice models... When the potential of interaction is long-ranged, these equations display a rich structure associated with canonical phase transitions and blow-up phenomena. In the limit of short-range interactions, they reduce to Cahn-Hilliard equations.
Keywords
Cite
@article{arxiv.cond-mat/0504716,
title = {Generalized Fokker-Planck equations and effective thermodynamics},
author = {Pierre-Henri Chavanis},
journal= {arXiv preprint arXiv:cond-mat/0504716},
year = {2009}
}