On the Question of Temperature Transformations under Lorentz and Galilei Boosts

TL;DR

This paper demonstrates that temperature, defined via thermodynamic equilibrium, cannot be transformed between inertial frames moving at constant velocities under Lorentz or Galilei boosts, restricting temperature to rest frames.

Contribution

It provides a quantum statistical thermodynamical proof that temperature cannot be transformed under Lorentz or Galilei boosts, resolving a long-standing debate.

Findings

Temperature is frame-invariant and only defined in a body's rest frame.

No temperature transformation laws exist under Lorentz or Galilei boosts.

A moving body cannot serve as a thermal reservoir in a different inertial frame.

Abstract

We provide a quantum statistical thermodynamical solution of the long standing problem of temperature transformations of uniformly moving bodies. Our treatment of this question is based on the well established quantum statistical result that the thermal equilibrium conditions demanded by both the Zeroth and Second Laws of Thermodynamics are precisely those of Kubo, Martin and Schwinger (KMS). We prove that, in both the special relativistic and nonrelativistic settings, a state of a body cannot satisfy these conditions for different inertial frames with non-zero relative velocity. Hence a body that serves as a thermal reservoir, in the sense of the Zeroth Law, in an inertial rest frame cannot do so in a laboratory frame relative to which it moves with non-zero uniform velocity. Consequently, there is no law of temperature transformation under either Lorentz or Galilei boosts, and so the concept of temperature stemming from the Zeroth Law is restricted to states of bodies in their rest frames.