Thermal time and TolmanEhrenfest effect: 'temperature as the speed of time'
Abstract
The notion of thermal time has been introduced as a possible basis for a fully generalrelativistic thermodynamics. Here we study this notion in the restricted context of stationary spacetimes. We show that the TolmanEhrenfest 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 TolmanEhrenfest relation, this one is free from any further dynamical assumption, thereby illustrating the physical import of the notion of thermal time.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 April 2011
 DOI:
 10.1088/02649381/28/7/075007
 arXiv:
 arXiv:1005.2985
 Bibcode:
 2011CQGra..28g5007R
 Keywords:

 General Relativity and Quantum Cosmology;
 Physics  Classical Physics
 EPrint:
 4 pages