Power-law ensembles: fluctuations of volume or temperature ?

TL;DR

This paper explores the equivalence between volume fluctuations at constant energy and Tsallis statistics with fluctuating temperature, showing how the nonextensivity parameter q relates to observable fluctuations in physical systems.

Contribution

It demonstrates the equivalence of volume fluctuations and Tsallis statistics with temperature fluctuations, and connects the nonextensivity parameter q to experimental fluctuation sum rules.

Findings

Volume fluctuations at constant energy are equivalent to Tsallis statistics with fluctuating temperature.

The nonextensivity parameter q relates to observable fluctuation sum rules.

Experimental data supports the connection between q and physical fluctuations.

Abstract

We present two issues here: (i) that in situation when total energy is kept constant recently proposed fluctuations of volume ensemble is equivalent to the approach using Tsallis statistics with fluctuating temperature and (ii) that the later (in which fluctuations are described by the nonextensivity parameter q) leads to the observed experimentally sum rule connecting fluctuations of different physical observables.