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...

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...

A procedure for deriving general nonlinear Fokker–Planck equations (FPEs) directly from the master equation is presented. The nonlinear effects are introduced in the transition probabilities, which present a dependence on the probabilities for finding the system in a given state. It is shown...

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...

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...

In this paper, a new class of weighted generalized beta distribution of the second kind (WGB2) is presented. The construction makes use of the conservability approach which includes the size or length-biased distribution as a special case. The class of WGB2 is used as descriptive models for the...