Thermodynamics, entropy, and stability of thin shells in 2+1 flat spacetimes

TL;DR

This paper investigates the thermodynamic properties and stability of a static thin shell in a (2+1)-dimensional flat spacetime, revealing that its entropy depends solely on its mass and is purely classical.

Contribution

It provides a novel analysis of the thermodynamics and stability of thin shells in 2+1 dimensions, deriving explicit entropy expressions and stability conditions.

Findings

Entropy depends only on the shell's mass.

Two explicit forms of entropy are derived.

Stability regions are characterized by parameter analysis.

Abstract

The thermodynamic equilibrium states of a static thin ring shell in a (2+1)-dimensional flat spacetime is analyzed. Inside the ring the spacetime is flat, whereas outside it is conical flat. The first law of thermodynamics applied to the thin shell leads to a shell's entropy which is a function of its mass alone. Two simple forms for this mass function are given leading to two different expressions for the entropy. The equations of thermodynamic stability are analyzed resulting in certain allowed regions for the free parameters. Contrary to the usual (3+1)-dimensional case this shell's entropy is purely classic, as the only fundamental constant that enters into the problem is the (2+1)-dimensional gravitational constant $G_3$, which has units of inverse mass.