Pathway Model, Superstatistics, Tsallis Statistics, and a Generalized Measure of Entropy

TL;DR

This paper links the pathway model to generalized entropy measures, showing its connections to Tsallis statistics, superstatistics, and fractional calculus, and explores its statistical properties and interpretations.

Contribution

It introduces a generalized entropy measure that derives the pathway model and unifies various entropy-based frameworks including Tsallis and superstatistics.

Findings

Pathway model inferred from a generalized entropy maximization

Connections established with Tsallis statistics and superstatistics

Probabilistic interpretations of the entropy measure

Abstract

The pathway model of Mathai (2005) is shown to be inferable from the maximization of a certain generalized entropy measure. This entropy is a variant of the generalized entropy of order 'alpha', considered in Mathai and Rathie (1975), and it is also associated with Shannon, Boltzmann-Gibbs, Renyi, Tsallis, and Havrda-Charvat entropies. The generalized entropy measure introduced here is also shown to haveinteresting statistical properties and it can be given probabilistic interpretations in terms of inaccuracy measure, expected value, and information content in a scheme. Particular cases of the pathway model are shown to be Tsallis statistics (Tsallis, 1988) and superstatistics introduced by Beck and Cohen (2003). The pathway model's connection to fractional calculus is illustrated by considering a fractional reaction equation.