Tolman's law in linear irreversible thermodynamics: a kinetic theory approach

TL;DR

This paper derives Tolman's law from relativistic kinetic theory, revealing the gravitational field's role as a cross effect similar to the Thomson effect, and generalizes the law for inhomogeneous media.

Contribution

It provides a kinetic theory derivation of Tolman's law and introduces a formal generalization for inhomogeneous media, highlighting the gravitational field as a cross effect.

Findings

Tolman's law can be derived from relativistic kinetic theory.

The gravitational field acts as a cross effect akin to the Thomson effect.

A formal generalization of Tolman's law for inhomogeneous media is established.

Abstract

In this paper it is shown that Tolman's law can be derived from relativistic kinetic theory applied to a simple fluid in a BGK-like approximation. Using this framework, it becomes clear that the contribution of the gravitational field can be viewed as a cross effect that resembles the so-called \emph{Thomson effect} in irreversible thermodynamics. A proper generalization of Tolman's law in an inhomogeneous medium is formally established based on these grounds.