Gravothermal Catastrophe and Tsallis' Generalized Entropy of Self-Gravitating Systems III. quasi-equilibrium structure using normalized q-values

TL;DR

This paper examines the thermodynamic properties of self-gravitating systems using Tsallis' non-extensive entropy with normalized q-values, confirming previous results on stellar polytropes and revealing new stability properties in thermal bath scenarios.

Contribution

It extends previous analyses by applying normalized q-expectation values, showing the quasi-equilibrium structure remains consistent and exploring stability criteria in different boundary conditions.

Findings

Stellar polytrope describes quasi-equilibrium states.

Thermodynamic stability aligns with negative specific heat.

New stability properties emerge with thermal bath boundary conditions.

Abstract

We revisit the issues on the thermodynamic property of stellar self-gravitating system arising from Tsallis' non-extensive entropy. Previous papers (Taruya & Sakagami, Physica A 307 (2002) 185 (cond-mat/0107494); ibid. (2002) in press (cond-mat/0204315)) have revealed that the extremum-state of Tsallis entropy characterized by the so-called stellar polytrope has consistent thermodynamic structure, which predicts the thermodynamic instability due to the negative specific heat. However, their analyses heavily relies on the old Tsallis formalism using standard linear mean values. In this paper, extending our previous study, we focus on the equilibrium structure based on the standard framework by means of the normalized q-expectation values. It then turns out that the new extremum-state of Tsallis entropy essentially remains unchanged from the previous result, i.e., the stellar quasi-equilibrium distribution can be described by the stellar polytrope. While the thermodynamic stability for a system confined in an adiabatic wall completely agrees with the previous study and thereby the stability/instability criterion remains unchanged, the stability analysis reveals a new equilibrium property for the system surrounded by a thermal bath. In any case, the stability/instability criteria are consistently explained from the presence of negative specific heat and within the formalism, the stellar polytrope is characterized as a plausible non-extensive meta-equilibrium state.