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

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)
PDF Full-text Download PDF Full-Text [302 KB, uploaded 1 November 2011 09:45 CET]
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

Article Statistics

Load and display the download statistics.

Citations to this Article

Cite This Article

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.

AMA Style

Ribeiro MS, Nobre FD, Curado EMF. Classes of N-Dimensional Nonlinear Fokker-Planck Equations Associated to Tsallis Entropy. Entropy. 2011; 13(11):1928-1944.

Chicago/Turabian Style

Ribeiro, Mauricio S.; Nobre, Fernando D.; Curado, Evaldo M. F. 2011. "Classes of N-Dimensional Nonlinear Fokker-Planck Equations Associated to Tsallis Entropy." Entropy 13, no. 11: 1928-1944.

Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert