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

Entropy

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

DOI  :  10.3390/e13111928

来源: DOAJ

【 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 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.

【 授权许可】

Unknown