title: Nonlinear inhomogeneous Fokker-Planck equations: Entropy and free-energy time evolution.
abstract: We extend a recently introduced free-energy formalism for homogeneous Fokker-Planck equations to a wide, and physically appealing, class of inhomogeneous nonlinear Fokker-Planck equations. In our approach, the free-energy functional is expressed in terms of an entropic functional and an auxiliary potential, both derived from the coefficients of the equation. With reference to the introduced entropic functional, we discuss the entropy production in a relaxation process towards equilibrium. The properties of the stationary solutions of the considered Fokker-Planck equations are also discussed.
authors.affiliation: Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud, 150, 22290-180, Rio de Janeiro, Brazil.
authors.forename: Gabriele
authors.initials: G
authors.lastname: Sicuro
authors.affiliation: Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud, 150, 22290-180, Rio de Janeiro, Brazil.
authors.forename: Peter
authors.initials: P
authors.lastname: Rapčan
authors.affiliation: Centro Brasileiro de Pesquisas Físicas, National Institute of Science and Technology for Complex Systems, Rua Dr. Xavier Sigaud, 150, 22290-180, Rio de Janeiro, Brazil and Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501, USA.
authors.forename: Constantino
authors.initials: C
authors.lastname: Tsallis