Statistical Thermodynamics of Moving Bodies

TL;DR

This paper uses quantum statistical methods to show that temperature is frame-dependent and only well-defined in a body's rest frame, challenging the idea of temperature transformation under relativity.

Contribution

It demonstrates that the zeroth law of thermodynamics applies only in a body's rest frame, using KMS conditions and modular theory, thus refuting temperature transformation under Lorentz boosts.

Findings

Temperature is frame-dependent and only well-defined in the rest frame.

No universal law of temperature transformation under Lorentz boosts.

Results also apply to nonrelativistic Galilean systems.

Abstract

We resolve the long standing question of temperature dependence of uniformly moving bodies by means of a quantum statistical treatment centred on the zeroth law of thermodynamics. The key to our treatment is the result, established by Kossakowski et al, that a macroscopic body behaves as a thermal reservoir with well-defined temperature, in the sense of the zeroth law, if and only if its state satisfies the Kubo-Martin-Schwinger (KMS) condition. In order to relate this result to the relativistic thermodynamics of moving bodies, we employ the Tomita-Takesaki modular theory to prove that a state cannot satisfy the KMS conditions with respect to two different inertial frames whose relative velocity is non-zero. This implies that the concept of temperature stemming from the zeroth law is restricted to states of bodies in their rest frames and thus that there is no law of temperature transformations under Lorentz boosts. The corresponding results for nonrelativistic Galilean systems have also been established.