We study the Markov property of processes described by generalized Fokker–Planck equations that are nonlinear with respect to probability densities such as mean field Fokker–Planck equations and Fokker–Planck equations related to generalized thermostatistics. We show that their transient...

Maximum entropy principle does not seem to distinguish between the use of Tsallis and Renyi entropies as either of them may be used to derive similar kind of q-exponential distributions. In this paper, we address the question whether the Renyi entropy is equally suitable to describe those...

General relations are found between the measure of the uniformity of distributions on the phase space and the first moments and correlations of extensive variables for systems close to thermal equilibrium. The role played by the parameter of the Renyi entropy for the analysis of their...

Product probability property, known in the literature as statistical independence, is examined first. Then generalized entropies are introduced, all of which give generalizations to Shannon entropy. It is shown that the nature of the recursivity postulate automatically determines the logarithmic...

It seems reasonable to consider concavity (with regard to all probability distributions) and stability (under arbitrarily small deformations of any given probability distribution) as necessary for an entropic form to be a physical one in the thermostatistical sense. Most known entropic forms,...

The Lesche stability condition for the Shannon entropy (J. Stat. Phys. 27 (1982) 419), represents a fundamental test, for its experimental robustness, for systems obeying the Maxwell–Boltzmann statistical mechanics. Of course, this stability condition must be satisfied by any entropic...

By solving a differential-functional equation inposed by the MaxEnt principle we obtain a class of two-parameter deformed logarithms and construct the corresponding two-parameter generalized trace-form entropies. Generalized distributions follow from these generalized entropies in the same...

Exact time-dependent solutions representing generalized one-dimensional Ornstein–Uhlenbeck processes are derived from nonlinear Fokker–Planck equations and the corresponding diffusion processes are studied. The corresponding systems are related to the Renyi entropy and entropies proposed by...

We show an interesting connection between non-standard (non-Boltzmannian) distribution functions arising in the theory of violent relaxation for collisionless stellar systems [D. Lynden-Bell, Mon. Not. R. Astron. Soc. 136 (1967) 101.] and the notion of superstatistics recently introduced by...

We discuss the main properties of general non-additive entropic forms based on arbitrary concave functions and their relation with the theory of majorization. As application, we examine the generalized entropic criterion for separability of mixed states of composite quantum systems, where...