Entropy Production and Equilibrium Conditions in General-Covariant Continuum Physics

TL;DR

This paper develops a general-covariant thermodynamics framework, establishing entropy relations and equilibrium conditions, emphasizing the necessity of Killing properties of the 4-temperature for equilibrium in curved spacetime.

Contribution

It introduces a covariant thermodynamics approach, deriving entropy identities and showing the Killing property is essential for equilibrium in general relativity.

Findings

Equilibrium requires the Killing property of the 4-temperature.

Non-dissipative materials are analyzed within this framework.

The entropy flux and production are formally derived in a covariant setting.

Abstract

Starting out with an entropy identity, the entropy flux, the entropy production and the corresponding Gibbs and Gibbs-Duhem equations of general-covariant conti\-nuum thermodynamics are established. Non-dissipative materials and equilibria are investigated. It is proved that equilibrium conditions only put on material properties cannot generate equilibria, rather additionally, the Killing property of the 4-temperature is a necessary condition for space-times in which equilibria are possible.