Stability analysis of the classical ideal gas in nonextensive statistics and the negative specific heat

TL;DR

This paper analyzes the stability of the classical ideal gas within nonextensive statistics, linking the nonextensive parameter to negative specific heat phenomena in self-gravitating systems.

Contribution

It provides a stability criterion based on Tsallis entropy, connecting the nonextensive parameter to negative specific heat in a novel way.

Findings

System is unstable for q>5/3

Negative specific heat occurs when the system is unstable

Stability condition matches the onset of negative specific heat

Abstract

We present a stability analysis of the classical ideal gas in a new theory of nonextensive statistics and use the theory to understand the phenomena of negative specific heat in some self-gravitating systems. The stability analysis is made on the basis of the second variation of Tsallis entropy. It is shown that the system is thermodynamically unstable if the nonextensive parameter is q>5/3, which is exactly equivalent to the condition of appearance of the negative specific heat.