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

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arxiv 1005.2985 v5 pith:QUITCGDB submitted 2010-05-17 gr-qc physics.class-ph

classification gr-qcphysics.class-ph
keywords timethermalnotiontemperaturetolman-ehrenfesteffectequilibriumspeed
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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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  1. Thermodynamics in space-times without horizons

    gr-qc 2025-07 conditional novelty 6.0 of 10

    Zero-energy timelike junction surfaces in static spherically symmetric spacetimes are shown to have area-proportional entropy and a temperature set by their transverse pressure.

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