Interpretation of the nonextensitivity parameter $q$ in some applications of Tsallis statistics and L\'evy distributions

TL;DR

This paper explains how the nonextensitivity parameter q in Tsallis statistics for q>1 is determined solely by fluctuations in the parameters of the exponential distribution, clarifying its interpretation.

Contribution

It provides a new understanding of the parameter q as arising from fluctuations in exponential distribution parameters within Tsallis statistics.

Findings

q is determined by fluctuations in exponential distribution parameters

Clarifies the interpretation of q in Tsallis statistics for q>1

Links q to the index of Le9vy distributions

Abstract

The nonextensitivity parameter $q$ occuring in some of the applications of Tsallis statistics (known also as index of the corresponding L\'evy distribution) is shown to be given, in $q>1$ case, entirely by the fluctuations of the parameters of the usual exponential distribution.