Invariant temperature of a moving body

Abstract

The temperature of a mechanical body has a kinetic interpretation: it describes the relative motion of particles within the body. Since the relative velocity of two particles is a Lorentz invariant, so is the temperature. In statistical physics, the temperature is defined as the inverse of the partial derivative of the entropy with respect to the internal energy (the energy in the rest frame of reference). Since the internal energy is a Lorentz invariant, so is the temperature. The Lorentz invariance of the temperature is a consequence of the symmetry between two bodies with equal proper temperatures, moving relative to one another with a constant relative speed, and in thermal contact. We give an equivalent, covariant definition of the temperature in terms of the energy and momentum of the body. We also note contradictions in the earlier articles that derived various transformation laws for the internal energy and temperature.