Tolman temperature gradients in a gravitational field

TL;DR

This paper examines Tolman's temperature gradients in gravitational fields, clarifying their conceptual basis, historical derivation, and relation to thermodynamics and the universality of free fall, addressing misconceptions across physics disciplines.

Contribution

It highlights the importance of the universality of free fall in understanding temperature gradients in gravitational equilibrium and revisits their possible derivation before general relativity.

Findings

Tolman temperature gradients are consistent with thermodynamics.

Temperature gradients in equilibrium can be derived without full general relativity.

The concept predates Einstein's general relativity, dating back to 1905.

Abstract

Tolman's relation for the temperature gradient in an equilibrium self-gravitating general relativistic fluid is broadly accepted within the general relativity community. However, the concept of temperature gradients in thermal equilibrium continues to cause confusion in other branches of physics, since it contradicts naive versions of the laws of classical thermodynamics. In this paper we discuss the crucial role of the universality of free fall, and how thermodynamics emphasises the great distinction between gravity and other forces. To do so we will present an argument given by Maxwell and apply it to an electro-thermal system, concluding with an reductio ad absurdum. Among other issues we shall show that Tolman temperature gradients could also (in principle) have been derived circa 1905 - a decade before the development of full general relativity.