On the use of non-canonical quantum statistics

TL;DR

This paper introduces a coarse-graining method for quantum energy fluctuations to better understand and compare Boltzmann-Gibbs and Tsallis statistics, highlighting the role of entropy in thermodynamics.

Contribution

It presents a novel coarse-graining approach to analyze quantum energy fluctuations and explores its implications for different statistical frameworks in thermodynamics.

Findings

Provides a unified parameterization of quantum energy fluctuations.

Offers insights into the relationship between Boltzmann-Gibbs and Tsallis statistics.

Discusses the foundational role of entropy and maximum entropy principle.

Abstract

We develop a method using a coarse graining of the energy fluctuations of an equilibrium quantum system which produces simple parameterizations for the behaviour of the system. As an application, we use these methods to gain more understanding on the standard Boltzmann-Gibbs statistics and on the recently developed Tsallis statistics. We conclude on a discussion of the role of entropy and the maximum entropy principle in thermodynamics.