Energy distribution and energy fluctuation in Tsallis statistics

TL;DR

This paper investigates energy distribution and fluctuations in Tsallis statistics using a new formalism, revealing ensemble nonequivalence for ideal gases and emphasizing the role of the nonextensive parameter q.

Contribution

It introduces a novel approach to calculating energy fluctuations in Tsallis statistics, differing from previous formulas, and explores their implications for ideal gases and finite heat baths.

Findings

Energy fluctuation cannot be neglected in the thermodynamic limit for ideal gases.

The new fluctuation formula differs from previous work but agrees under certain conditions.

The nonextensive parameter q significantly influences energy fluctuations in finite systems.

Abstract

The energy distribution and the energy fluctuation in the Tsallis canonical ensemble are studied with the OLM formalism but following a new way. The resulting formula for the energy fluctuation is not the same as that in previous work [Liu L.Y. and Du J.L., Physica A 387(2008)5417]. In discussing the application of an ideal gas, we find that the energy fluctuation can not be negligible in the thermodynamic limit, showing the ensemble nonequivalence for this case in Tsallis statistics. We investigate the energy fluctuation with a Tsallis generalized canonical distribution studied by Plastino and Plastino [Phys. Lett. A 193(1994)140] for describing a system in contact with a finite heath bath. For this situation, the two formulae for the energy fluctuation are shown to be equivalent, while the nonextensive parameter q plays a very important role.