Thermal time and TolmanEhrenfest effect: temperature as the speed of time
Résumé
The notion of thermal time has been introduced as a possible basis for a fully general-relativistic thermodynamics. Here we study this notion in the restricted context of stationary spacetimes. We show that the Tolman-Ehrenfest effect (in a stationary gravitational field, temperature is not constant in space at thermal equilibrium) can be derived very simply by applying the equivalence principle to a key property of thermal time at equilibrium: temperature is the rate of thermal time with respect to proper time - the 'speed of (thermal) time '. Unlike other published derivations of the Tolman-Ehrenfest law, this one is free from any further dynamical assumption, thereby illustrating the physical import of the notion of thermal time.
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