A general maximum entropy principle for self-gravitating perfect fluid

TL;DR

This paper demonstrates that the extremization of entropy in a self-gravitating perfect fluid system naturally leads to the TOV equation, establishing a deep connection between thermodynamics and general relativity.

Contribution

It proves that the relativistic TOV equation can be derived from a maximum entropy principle for perfect fluids, extending to charged fluids and highlighting the thermodynamic foundation of gravitational equilibrium.

Findings

Extremizing entropy yields the TOV equation.

Generalized TOV equation derived for charged fluids.

Supports the link between thermodynamics and gravity.

Abstract

We consider a self-gravitating system consisting of perfect fluid with spherical symmetry. Using the general expression of entropy density, we extremize the total entropy $S$ under the constraint that the total number of particles is fixed. We show that extrema of $S$ coincides precisely with the relativistic Tolman-Oppenheimer-Volkoff (TOV) equation of hydrostatic equilibrium. Furthermore, we apply the maximum entropy principle to a charged perfect fluid and derive the generalized TOV equation. Our work provides a strong evidence for the fundamental relationship between general relativity and ordinary thermodynamics.