Fluctuation theorems in nonextensive statistics

TL;DR

This paper explores how fluctuation theorems can be applied within nonextensive statistics to derive properties of $q$-canonical ensembles, revealing conditions on the parameter $q$ based on the system's density of states.

Contribution

It introduces the use of fluctuation theorems in nonextensive statistics to analyze $q$-canonical ensembles and establishes conditions on $q$ related to the density of states.

Findings

Derived conditions for the values of q based on the density of states

Applied fluctuation theorems to nonextensive statistical mechanics

Provided a framework for analyzing power-law distributions

Abstract

Nonextensive statistics is a formalism of statistical mechanics that describes the ocurrence of power-law distributions in complex systems, particularly the so-called $q$ exponential family of distributions. In this work we present the use of fluctuation theorems for $q$-canonical ensembles as a powerful tool to readily obtain statistical properties. In particular, we have obtained strong conditions for the possible values of $q$ depending on the density of states of the system.