# Thermodynamical stability for perfect fluid

## TL;DR

This paper establishes a thermodynamic stability criterion for self-gravitating perfect fluids, linking thermodynamics with gravitational stability and extending previous results to more general cases.

## Contribution

It derives a new thermodynamic stability criterion for perfect fluids that aligns with dynamical stability results and applies beyond spherical symmetry.

## Key findings

- Thermodynamic stability criterion matches Chandrasekhar and Wald's dynamical stability.
- Criterion applies to non-spherical and general perturbations.
- Connects thermodynamics with gravitational stability.

## Abstract

According to maximum entropy principle, it has been proved that the gravitational field equations could be derived by the extrema of total entropy for perfect fluid, which implies that thermodynamic relations contain information of gravity. In this manuscript, we obtain a criterion for thermodynamical stability of an adiabatic, self-gravitating perfect fluid system by the second variation of total entropy. We show, for Einstein's gravity with spherical symmetry spacetime, that the criterion is consistent with that for dynamical stability derived by Chandrasekhar and Wald. We also find that the criterion could be applied to cases without spherical symmetry, or under general perturbations. The result further establishes the connection between thermodynamics and gravity.