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

Entropy

Mauricio S. Ribeiro¹  Fernando D. Nobre¹ 

[1] Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud 150, 22290-180, Rio de Janeiro, RJ, Brazil; E-Mails:

关键词: nonlinear Fokker-Planck equations;    H-theorem;    nonextensive thermostatistics;   

DOI  :  10.3390/e13111928

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY   
© 2011 by the authors; licensee MDPI, Basel, Switzerland.