Entropy Production in Relativistic Binary Mixtures

TL;DR

This paper calculates the entropy production in a relativistic binary gas mixture using kinetic theory and Chapman-Enskog expansion, confirming it can be expressed as flux-force bilinear forms consistent with thermodynamics.

Contribution

It provides a covariant kinetic theory derivation of entropy production in relativistic mixtures, extending non-relativistic thermodynamics to relativistic regimes.

Findings

Entropy production expressed as flux-force bilinear form.

Covariant form of Boltzmann's equation used.

First-order Chapman-Enskog expansion applied.

Abstract

In this paper we calculate the entropy production of a relativistic binary mixture of inert dilute gases using kinetic theory. For this purpose we use the covariant form of Boltzmann's equation which, when suitably transformed, yields a formal expression for such quantity. Its physical meaning is extracted when the distribution function is expanded in the gradients using the well-known Chapman-Enskog method. Retaining the terms to first order, consistently with Linear Irreversible Thermodynamics we show that indeed, the entropy production can be expressed as a bilinear form of products between the fluxes and their corresponding forces. The implications of this result are thoroughly discussed.