On the validity of the Onsager relations in relativistic binary mixtures

TL;DR

This paper investigates the validity of Onsager reciprocity relations in relativistic binary mixtures, analyzing the role of pressure gradients and proposing alternative Onsager matrices consistent with these relations.

Contribution

It introduces two alternative Onsager matrices for relativistic mixtures that satisfy reciprocity relations and examines the inadequacy of chemical potential as a thermodynamic force.

Findings

Proposed two Onsager matrices compatible with reciprocity.

Identified pressure gradient effects in relativistic mixtures.

Highlighted limitations of chemical potential as a thermodynamic force.

Abstract

In this work we study the properties of a relativistic mixture of two non-reacting dilute species in thermal local equilibrium. Following the conventional ideas in kinetic theory, we use the concept of chaotic velocity. In particular, we address the nature of the density, or pressure gradient term that arises in the solution of the linearized Boltzmann equation in this context. Such effect, also present for the single component problem, has so far not been analyzed from the point of view of the Onsager resciprocity relations. In order to address this matter, we propose two alternatives for the Onsagerian matrix which comply with the corresponding reciprocity relations and also show that, as in the non-relativistic case, the chemical potential is not an adequate thermodynamic force. The implications of both representations are briefly analyzed.