Self-gravitating Stellar Systems and Non-extensive Thermostatistics

TL;DR

This paper applies Tsallis' non-extensive entropy to self-gravitating stellar systems, deriving a new equation of state and analyzing thermodynamic stability and quasi-equilibrium states through simulations.

Contribution

It introduces a novel application of Tsallis entropy to model the thermodynamics of self-gravitating systems, including deriving the stellar polytrope and analyzing stability.

Findings

Derivation of the stellar polytrope from Tsallis entropy

Identification of thermodynamic instability due to negative specific heat

Confirmation of quasi-equilibrium states via N-body simulations

Abstract

After introducing the fundamental properties of self-gravitating systems, we present an application of Tsallis' generalized entropy to the analysis of their thermodynamic nature. By extremizing the Tsallis entropy, we obtain an equation of state known as the stellar polytrope. For a self-gravitating stellar system confined within a perfectly reflecting wall, we discuss the thermodynamic instability caused by its negative specific heat. The role of the extremum as a quasi-equilibrium is also demonstrated from the results of N-body simulations.