Canonical Ensemble in Non-extensive Statistical Mechanics

TL;DR

This paper explores the canonical ensemble within non-extensive statistical mechanics, using a traditional approach with a reservoir characterized by generalized entropy, to deepen understanding of its applicability.

Contribution

It derives the equations of non-extensive statistical mechanics through a traditional microstate probability approach, offering new insights into its foundational basis.

Findings

Derivation of non-extensive equations using microstate probabilities

Insight into the applicability of non-extensive statistics

Comparison with traditional thermodynamic approaches

Abstract

The framework of non-extensive statistical mechanics, proposed by Tsallis, has been used to describe a variety of systems. The non-extensive statistical mechanics is usually introduced in a formal way, using the maximization of entropy. In this article we investigate the canonical ensemble in the non-extensive statistical mechanics using a more traditional way, by considering a small system interacting with a large reservoir via short-range forces. The reservoir is characterized by generalized entropy instead of the Boltzmann-Gibbs entropy. Assuming equal probabilities for all available microstates we derive the equations of the non-extensive statistical mechanics. Such a procedure can provide deeper insight into applicability of the non-extensive statistics.