Proving the Lorentz invariance of the entropy and the covariance of thermodynamics

TL;DR

This paper proves that thermodynamic entropy is Lorentz invariant and thermodynamics is covariant, based on fundamental assumptions about inertial frames and Lorentz-invariant microscopic theories, applicable in both classical and quantum physics.

Contribution

It provides a rigorous proof of the Lorentz invariance of entropy without relying on probability, strengthening the foundations of relativistic thermodynamics.

Findings

Entropy is Lorentz invariant in equilibrium.

Adiabatic transformations can accelerate bodies without changing rest mass.

Thermodynamics laws are derived as Lorentz invariant from microscopic theory.

Abstract

The standard argument for the Lorentz invariance of the thermodynamic entropy in equilibrium is based on the assumption that it is possible to perform an adiabatic transformation whose only outcome is to accelerate a macroscopic body, keeping its rest mass unchanged. The validity of this assumption constitutes the very foundation of relativistic thermodynamics and needs to be tested in greater detail. We show that, indeed, such a transformation is always possible, at least in principle. The only two assumptions invoked in the proof are that there is at least one inertial reference frame in which the second law of thermodynamics is valid and that the microscopic theory describing the internal dynamics of the body is a field theory, with Lorentz invariant Lagrangian density. The proof makes no reference to the connection between entropy and probabilities and is valid both within classical and quantum physics. To avoid any risk of circular reasoning, we do not postulate that the laws of thermodynamics are the same in every reference frame, but we obtain this fact as a direct consequence of the Lorentz invariance of the entropy.