title: Consequences of the H theorem from nonlinear Fokker-Planck equations.
abstract: A general type of nonlinear Fokker-Planck equation is derived directly from a master equation, by introducing generalized transition rates. The H theorem is demonstrated for systems that follow those classes of nonlinear Fokker-Planck equations, in the presence of an external potential. For that, a relation involving terms of Fokker-Planck equations and general entropic forms is proposed. It is shown that, at equilibrium, this relation is equivalent to the maximum-entropy principle. Families of Fokker-Planck equations may be related to a single type of entropy, and so, the correspondence between well-known entropic forms and their associated Fokker-Planck equations is explored. It is shown that the Boltzmann-Gibbs entropy, apart from its connection with the standard--linear Fokker-Planck equation--may be also related to a family of nonlinear Fokker-Planck equations.
authors.affiliation: Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro, Rio de Janeiro, Brazil. veit@cbpf.br
authors.forename: Veit
authors.initials: V
authors.lastname: Schwämmle
authors.forename: Fernando D
authors.initials: FD
authors.lastname: Nobre
authors.forename: Evaldo M F
authors.initials: EM
authors.lastname: Curado