Equivalence among different formalisms in the Tsallis entropy framework

Details Equivalence among different formalisms in the Tsallis entropy framework Equivalence among different formalisms in the Tsallis entropy framework

2006-08-05

arxiv.org/abs/cond-mat/0608138v2

Physics

Condensed Matter

Statistical Mechanics

20 pages, 1 figure, Elsart macro style, version accepted on Physica A

Scientific paper

10.1016/j.physa.2007.05.029

In a recent paper [Phys. Lett. A {\bf335}, 351 (2005)] the authors discussed the equivalence among the various probability distribution functions of a system in equilibrium in the Tsallis entropy framework. In the present letter we extend these results to a system which is out of equilibrium and evolves to a stationary state according to a nonlinear Fokker-Planck equation. By means of time-scale conversion, it is shown that there exists a ``correspondence'' among the self-similar solutions of the nonlinear Fokker-Planck equations associated with the different Tsallis formalisms. The time-scale conversion is related to the corresponding Lyapunov functions of the respective nonlinear Fokker-Planck equations.

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