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Entropy 2011, 13(11), 1928-1944; doi:10.3390/e13111928
Article

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

1,* , 1,2
 and 1,2,3
1 Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud 150, 22290-180, Rio de Janeiro, RJ, Brazil 2 National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150, 22290-180, Rio de Janeiro, RJ, Brazil 3 Laboratoire APC, Université Paris Diderot, 10, rue A. Domon et L. Duquet, 75205, Paris, France
* Author to whom correspondence should be addressed.
Received: 4 October 2011 / Accepted: 21 October 2011 / Published: 1 November 2011
(This article belongs to the Special Issue Tsallis Entropy)
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Abstract

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.
Keywords: nonlinear Fokker-Planck equations; H-theorem; nonextensive thermostatistics nonlinear Fokker-Planck equations; H-theorem; nonextensive thermostatistics
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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MDPI and ACS Style

Ribeiro, M.S.; Nobre, F.D.; Curado, E.M.F. Classes of N-Dimensional Nonlinear Fokker-Planck Equations Associated to Tsallis Entropy. Entropy 2011, 13, 1928-1944.

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