Thermodynamic equilibrium condition and the first law of thermodynamics for charged perfect fluids in electromagnetic and gravitational fields

TL;DR

This paper establishes the precise conditions under which a charged perfect fluid in electromagnetic and gravitational fields reaches thermodynamic equilibrium, and derives the first law of thermodynamics for such charged stars.

Contribution

It provides a rigorous proof of equilibrium conditions and formulates the first law of thermodynamics for charged fluids in dynamic fields, extending previous static analyses.

Findings

Necessary and sufficient conditions for thermodynamic equilibrium in dynamic fields

Explicit expression for the first law of thermodynamics for charged stars

Generalization of equilibrium conditions beyond fixed field scenarios

Abstract

We provide a proof of the necessary and sufficient condition on the profile of the temperature, chemical potential, and angular velocity for a charged perfect fluid in dynamic equilibrium to be in thermodynamic equilibrium not only in fixed but also in dynamical electromagnetic and gravitational fields. In passing, we also present the corresponding expression for the first law of thermodynamics for such a charged star.