Energy fluctuations and the ensemble equivalence in Tsallis statistics

TL;DR

This paper examines energy fluctuations in Tsallis statistics, demonstrating that for large particle numbers, the relative energy fluctuation diminishes as 1/N, preserving ensemble equivalence unlike in traditional Boltzmann-Gibbs statistics.

Contribution

It shows that ensemble equivalence persists in Tsallis statistics with energy fluctuations decreasing as 1/N for large systems, contrasting with classical results.

Findings

Relative energy fluctuation scales as 1/N in Tsallis statistics

Ensemble equivalence holds in Tsallis framework for large N

Energy fluctuations differ from Boltzmann-Gibbs predictions

Abstract

We investigate the general property of the energy fluctuation for the canonical ensemble in Tsallis statistics and the ensemble equivalence. By taking the ideal gas and the non-interacting harmonic oscillators as examples, we show that, when the particle number N is large enough, the relative fluctuation of the energy is proportional to 1/N in the new statistics, instead of square root of 1/N in Boltzmann-Gibbs statistics. Thus the equivalence between the microcanonical and the canonical ensemble still holds in Tsallis statistics.