We work out a superstatistical description of high-energy scattering processes that takes into account temperature fluctuations in small-volume elements. For Γ -distributed fluctuations of the inverse temperature one effectively obtains a generalized statistical mechanics of Tsallis type, whereas for other temperature distributions more general superstatistical models arise. We consider two mai...

In this paper, we will study the large scale structure formation using gravitational partition function. We assertively argue that system of gravitating galaxies can be analyzed Tsallis statistical mechanics. The divergences in function removed mathematical riches generalization dimensional regularization (GDR). finite thus obtained used to evaluate thermodynamics and thus, understand clusterin...

There are two disparate formulations of the entropic lattice Boltzmann scheme: one of these theories revolves around the analog of the discrete Boltzmann H function of standard extensive statistical mechanics, while the other revolves around the nonextensive Tsallis entropy. It is shown here that it is the nonenforcement of the pressure tensor moment constraints that lead to extremizations of e...

Stationary and time-dependent solutions of a nonlinear Kramers equation, as well as its associated nonlinear Fokker-Planck equations, are investigated within the context of Tsallis nonextensive statistical mechanics. Since no general analytical time-dependent solutions are found for such a nonlinear Kramers equation, an ansatz is considered and the corresponding asymptotic behavior is studied a...

We present a study of both the “Iterative Procedure” and the “β → β transformation”, proposed by Tsallis et al (Physica A261, 534) to find the probabilities pi of a system to be in a state with energy ǫi, within the framework of a generalized statistical mechanics. Using stability and convexity arguments, we argue that the iterative procedure does not always provide the right temperature depend...

The laws of thermodynamics constrain the formulation of statistical mechanics at the microscopic level. The third law of thermodynamics states that the entropy must vanish at absolute zero temperature for systems with nondegenerate ground states in equilibrium. Conversely, the entropy can vanish only at absolute zero temperature. Here we ask whether or not generalized entropies satisfy this fun...

In nonextensive statistical mechanics, two kinds of definitions have been considered for expectation value of a physical quantity: one is the ordinary definition and the other is the normalized q-expectation value employing the escort distribution. Since both of them lead to the maximum-Tsallis-entropy distributions of a similar type, it is of crucial importance to determine which the correct p...

Triangle for the entropic index q of non-extensive statistical mechanics observed by Voyager 1 in the distant heliosphere Abstract Tsallis [Physica A 340 (2004) 1] identified a set of numbers, the ''q-triplet'' {q stat , q sen , q rel }, for a system described by nonextensive statistical mechanics. The deviation of the q's from unity is a measure of the departure from thermodynamic equilibrium....

Tsallis and Rényi entropy measures are two possible different generalizations of the Boltzmann-Gibbs entropy (or Shannon’s information) but are not generalizations of each others. It is however the Sharma-Mittal measure, which was already defined in 1975 (B.D. Sharma, D.P. Mittal, J.Math.Sci 10, 28) and which received attention only recently as an application in statistical mechanics (T.D. Fran...