Tolman temperature gradients in a gravitational field

Understand

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.