相关论文: Pathway Model, Superstatistics, Tsallis Statistics…

The pathway model of Mathai (2005) mainly deals with the rectangular matrix-variate case. In this paper the scalar version is shown to be associated with a large number of probability models used in physics. Different families of densities…

We presented background information about various entropies in the literature. The pathway idea of Mathai (2005) is shown to be inferable from the maximization of a certain generalized entropy measure and established connections to…

An entropy for the scalar variable case, parallel to Havrda-Charvat entropy was introduced by the first author and the properties and its connection to Tsallis non-extensive statistical mechanics and the Mathai pathway model were examined…

Superstatistics and Tsallis statistics in statistical mechanics is given an interpretation in terms of Bayesian statistical analysis. Subsequently superstatistics is extended by replacing each component of the conditional and marginal…

In a paper [8] the authors classify entropy into three categories, as a thermodynamics quantity, as a measure of information production, and as a means of statistical inference. An entropy measure introduced by Mathai falls into the second…

Tsallis and R\'{e}nyi 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…

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…

In reaction rate theory, in input-output type models and in reaction-diffusion problems when the total derivatives are replaced by fractional derivatives the solutions are obtained in terms of Mittag-Leffler functions and their…

Pathway idea is a switching mechanism by which one can go from one functional form to another, and to yet another. It is shown that through a parameter $\alpha$, called the pathway parameter, one can connect generalized type-1 beta family…

A general principle called "conservation of the ellipsoid of concentration" is introduced and a generalized entropic form of order 'alpha' is optimized under this principle. It is shown that this can produce a density which can act as a…

The Tsallis entropy given for a positive parameter $\alpha$ can be considered as a modification of the classical Shannon entropy. For the latter, corresponding to $\alpha=1$, there exist many axiomatic characterizations. One of them based…

Entropy and relative or cross entropy measures are two very fundamental concepts in information theory and are also widely used for statistical inference across disciplines. The related optimization problems, in particular the maximization…

Recently, a new measure of information called extropy has been introduced by Lad, Sanfilippo and Agr\`o as the dual version of Shannon entropy. In the literature, Tsallis introduced a measure for a discrete random variable, named Tsallis…

The Tsallis entropy, which is a generalization of the Boltzmann-Gibbs entropy, plays a central role in nonextensive statistical mechanics of complex systems. A lot of efforts have recently been made on establishing a dynamical foundation…

We investigate the cumulative Tsallis entropy, an information measure recently introduced as a cumulative version of the classical Tsallis differential entropy, which is itself a generalization of the Boltzmann-Gibbs statistics. This…

We propose a new way of defining entropy of a system, which gives a general form which may be nonextensive as Tsallis entropy, but is linearly dependent on component entropies, like Renyi entropy, which is extensive. This entropy has a…

In reaction rate theory, in production-destruction type models and in reaction-diffusion problems when the total derivatives are replaced by fractional derivatives the solutions are obtained in terms of Mittag-Leffler functions and their…

We find the value of constants related to constraints in characterization of some known statistical distributions and then we proceed to use the idea behind maximum entropy principle to derive generalized version of this distributions using…

A general investigation is made into the intrinsic Riemannian geometry for complex systems, from the perspective of statistical mechanics. The entropic formulation of statistical mechanics is the ingredient which enables a connection…

The formalism of statistical mechanics can be generalized by starting from more general measures of information than the Shannon entropy and maximizing those subject to suitable constraints. We discuss some of the most important examples of…