Entropy Identity and Material-Independent Equilibrium Conditions in Relativistic Thermodynamics

TL;DR

This paper develops a general relativistic thermodynamics framework using an entropy density 4-vector, deriving material-independent equilibrium conditions that unify and extend previous approaches in special and general relativity.

Contribution

It introduces a comprehensive entropy density 4-vector and derives universal equilibrium conditions applicable to various space-time geometries in relativistic thermodynamics.

Findings

Established a general entropy density 4-vector framework.

Derived material-independent equilibrium conditions.

Unified conditions for thermodynamic equilibrium in relativistic settings.

Abstract

On the basis of the balance equations for energy-momentum, spin, particle and entropy density, an approach is considered which represents a comparatively general framework for special- and general-relativistic continuum thermodynamics. In the first part of the paper, a general entropy density 4-vector, containing particle, energy-momentum, and spin density contributions, is introduced which makes it possible, firstly, to judge special assumptions for the entropy density 4-vector made by other authors with respect to their generality and validity and, secondly, to determine entropy supply and entropy production. Using this entropy density 4-vector, in the second part, material-independent equilibrium conditions are discussed. While in literature, at least if one works in the theory of irreversible thermodynamics assuming a Riemann space-time structure, generally thermodynamic equilibrium is determined by introducing a variety of conditions by hand, the present approach proceeds as follows: For a comparatively wide class of space-time geometries the necessary equilibrium conditions of vanishing entropy supply and entropy production are exploited and, afterwards, supplementary conditions are assumed which are motivated by the requirement that thermodynamic equilibrium quantities have to be determined uniquely.