Classes of \(N\)-dimensional nonlinear Fokker-Planck equations associated to Tsallis entropy (Q400957)

Summary: Several previous results valid for one-dimensional nonlinear Fokker-Planck equations are generalized to \(N\)-dimensions. A general nonlinear \(N\)-dimensional Fokker-Planck equation is derived directly from a master equation, by considering nonlinearities in the transition rates. Using nonlinear Fokker-Planck equations, the H-theorem is proved; for that, an important relation involving these equations and general entropic forms is introduced. It is shown that due to this relation, classes of nonlinear \(N\)-dimensional Fokker-Planck equations are connected to a single entropic form. A particular emphasis is given to the class of equations associated to Tsallis entropy, in both cases of the standard, and generalized definitions for the internal energy.