Canonical ensemble in non-extensive statistical mechanics when q>1

TL;DR

This paper explores the canonical ensemble in non-extensive statistical mechanics for q>1, addressing divergence issues and establishing limits on microstate growth, providing physical insights beyond entropy maximization.

Contribution

It investigates the canonical ensemble with q>1, clarifies divergence problems, and derives a universal limit on microstate growth in non-extensive systems.

Findings

Identifies divergence issues for q>1 in non-extensive mechanics.

Establishes a universal limit on the number of microstates.

Provides physical interpretation beyond entropy maximization.

Abstract

The non-extensive statistical mechanics has been used to describe a variety of complex systems. The maximization of entropy, often used to introduce the non-extensive statistical mechanics, is a formal procedure and does not easily leads to physical insight. In this article we investigate the canonical ensemble in the non-extensive statistical mechanics by considering a small system interacting with a large reservoir via short-range forces and assuming equal probabilities for all available microstates. We concentrate on the situation when the reservoir is characterized by generalized entropy with non-extensivity parameter q>1. We also investigate the problem of divergence in the non-extensive statistical mechanics occurring when q>1 and show that there is a limit on the growth of the number of microstates of the system that is given by the same expression for all values of q.