Relativistic thermodynamics of perfect fluids

TL;DR

This paper develops a covariant relativistic thermodynamic framework for perfect fluids, deriving transformation laws and equations that incorporate relativistic effects on heat, work, and inertia.

Contribution

It introduces a covariant formulation of relativistic thermodynamics for perfect fluids, including new transformation laws and continuity equations based on Minkowski space.

Findings

Derived relativistic continuity equations for thermodynamic quantities.

Identified relativistic corrections in Euler and continuity equations.

Established transformation laws for temperature, pressure, and chemical potential.

Abstract

The relativistic continuity equations for the extensive thermodynamic quantities are derived based on the divergence theorem in Minkowski space outlined by St\"uckelberg. This covariant approach leads to a relativistic formulation of the first and second laws of thermodynamics. The internal energy density and the pressure of a relativistic perfect fluid carry inertia, which leads to a relativistic coupling between heat and work. The relativistic continuity equation for the relativistic inertia is derived. The relativistic corrections in the Euler equation and in the continuity equations for the energy and momentum are identified. This relativistic theoretical framework allows a rigorous derivation of the relativistic transformation laws for the temperature, the pressure and the chemical potential based on the relativistic transformation laws for the energy density, the entropy density, the mass density and the number density.