Covariant Relativistic Non-Equilibrium Thermodynamics of Multi-Component Systems

TL;DR

This paper develops a covariant framework for relativistic non-equilibrium thermodynamics in multi-component systems, deriving key quantities and equilibrium conditions, including the multi-component Killing relation of the 4-temperature, with applications to gravitating mixtures.

Contribution

It introduces a covariant approach to relativistic multi-component thermodynamics, deriving fundamental quantities and equilibrium conditions, and analyzing gravitating mixtures.

Findings

Derived energy-momentum tensors for components and mixtures

Established equilibrium conditions and Killing relation for 4-temperature

Analyzed gravitating multi-component systems

Abstract

Non-equilibrium and equilibrium thermodynamics of an interacting component in a relativistic multi-component system is discussed covariantly by exploiting an entropy identity. The special case of the corresponding free component is considered. Equilibrium conditions and especially the multi-component Killing relation of the 4-temperature are discussed. Two axioms characterize the mixture: additivity of the energy momentum tensors and additivity of the 4-entropies of the components generating those of the mixture. The resulting quantities of a single component and of the mixture as a whole, energy, energy flux, momentum flux, stress tensor, entropy, entropy flux, supply and production are derived. Finally, a general relativistic 2-component mixture is discussed with respect to their gravitation generating energy-momentum tensors.