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arXiv · 1005.2985

Thermal time and the Tolman-Ehrenfest effect: temperature as the "speed of time"

Carlo Rovelli·Matteo Smerlak
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Abstract

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 relation, this one is free from any further dynamical assumption, thereby illustrating the physical import of the notion of thermal time.

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Carlo Rovelli, Matteo Smerlak. 2011-01-18. Thermal time and the Tolman-Ehrenfest effect: temperature as the "speed of time". https://doi.org/10.1088/0264-9381%2F28%2F7%2F075007

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