Thermodynamic equilibrium with acceleration and the Unruh effect

TL;DR

This paper investigates the conditions for thermodynamic equilibrium in accelerating quantum fields, demonstrating that the Unruh temperature sets a fundamental lower limit for the temperature of accelerated fluids.

Contribution

It establishes that the Unruh temperature is an absolute lower bound for equilibrium temperatures in accelerated quantum systems, extending understanding of thermodynamics in relativistic contexts.

Findings

Mean values vanish at the Unruh temperature after vacuum subtraction

Unruh temperature acts as a lower bound for accelerated fluid temperatures

Conditions for local thermodynamic equilibrium are discussed

Abstract

We address the problem of thermodynamic equilibrium with constant acceleration along the velocity field lines in a quantum relativistic statistical mechanics framework. We show that for a free scalar quantum field, after vacuum subtraction, all mean values vanish when the local temperature T is as low as the Unruh temperature T_U = A/2\pi where A is the magnitude of the acceleration four-vector. We argue that the Unruh temperature is an absolute lower bound for the temperature of any accelerated fluid at global thermodynamic equilibrium. We discuss the conditions of this bound to be applicable in a local thermodynamic equilibrium situation.