Equivalence among different formalisms in the Tsallis entropy framework

A.M. Scarfone and T. Wada

Physica A: Statistical Mechanics and its Applications, 2007, vol. 384, issue 2, 305-317

Abstract: In a recent paper [T. Wada, A.M. Scarfone, Phys. Lett. A 335 (2005) 351] 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 (NFPE). By means of time-scale conversion, it is shown that there exists a “correspondence” among the self-similar solutions of the NFPEs associated with the different Tsallis formalisms. The time-scale conversion is related to the corresponding Lyapunov functions of the respective NFPEs.

Keywords: Tsallis entropy; Nonlinear Fokker–Planck equation; Escort probability; Lyapunov function (search for similar items in EconPapers)
Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:384:y:2007:i:2:p:305-317

DOI: 10.1016/j.physa.2007.05.029

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