In correspondence to conventional thermostatistics we formulate an H-theorem showing that transients solutions of nonlinear Fokker–Planck equations related to generalized thermostatistics converge to stationary probability densities. The H-theorem is applied to relaxation processes of...

The present study extends the correspondence principle of Martinez et al. that establishes a link between nonlinear Fokker–Planck equations (NLFPEs) and the variational principle approach of the theory of canonical ensembles. By virtue of the extended correspondence principle we reobtain...

In this paper, we have analyzed the nonextensive Tsallis statistical mechanics in the light of Verlinde’s formalism. We have obtained, with the aid of a noncommutative phase–space entropic gravity, a new bound for Tsallis nonextensive (NE) parameter (TNP) that is clearly different from the...

Multivariate nonlinear Fokker–Planck equations are derived which are solved by equilibrium distributions of generalized thermostatistics. The multivariate Fokker–Planck equations proposed by Kaniadakis and by Borland et al. are re-obtained as special cases. Furthermore, a Kramers equation is...

We examine postural sway data using concepts of nonextensive thermostatistics. We show that nonextensive thermostatistical cutoff distributions fit approximately empirically observed distributions of postural sway data. We show that the index of nonextensivity of these cutoff distributions is...

We numerically study, at the edge of chaos, the behaviour of the single-site map xt+1=xt−xt/(x2t+γ2), where γ is the map parameter.

We study the relationship between chaotic behavior and the Central Limit Theorem (CLT) in the Kuramoto model. We calculate sums of angles at equidistant times along deterministic trajectories of single oscillators and we show that, when chaos is sufficiently strong, the Pdfs of the sums tend to...

The purpose of this comment is to correct mistaken assumptions and claims made in the paper “Stochastic feedback, nonlinear families of Markov processes, and nonlinear Fokker–Planck equations” by T. D. Frank [T.D. Frank, Stochastic feedback, non-linear families of Markov processes, and...

The sensitivity to initial conditions and relaxation dynamics of two-dimensional maps are analyzed at the edge of chaos, along the lines of nonextensive statistical mechanics. We verify the dual nature of the entropic index for the Henon map, one (qsen<1) related to its sensitivity to initial condition properties, and the other, graining-dependent (qrel(W)>1), related to its relaxation dynamics...</1)>

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...