Equivalence among different formalisms in the Tsallis entropy framework

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.