Statistical thermodynamics of moving bodies *

We resolve the long-standing question of temperature transformations of uniformly moving bodies by means of a quantum statistical treatment centered 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 condition with respect to two different inertial frames whose relative velocity is nonzero. 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.