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Classes of N-Dimensional Nonlinear Fokker-Planck Equations Associated to Tsallis Entropy

2011; Multidisciplinary Digital Publishing Institute; Volume: 13; Issue: 11 Linguagem: Inglês

10.3390/e13111928

1099-4300

Maurício Serra Ribeiro, Fernando Nobre, Evaldo M. F. Curado,

Complex Systems and Time Series Analysis

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 nonlinearitiesin 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.