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

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

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. View Full-Text
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 (CC BY 3.0).

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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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