T' = T, S' = gamma S, P'= gamma^2 P, V'= V/gamma, and U' = gamma U

TL;DR

This paper demonstrates the correct relativistic transformation laws for thermodynamic quantities such as temperature, entropy, pressure, volume, and energy, ensuring consistency with Lorentz invariance in relativistic thermodynamics.

Contribution

It establishes the proper Lorentz transformation rules for thermodynamic variables of an ideal gas, clarifying their behavior under relativistic motion.

Findings

Temperature remains invariant under Lorentz transformations.

Entropy scales with gamma factor, S' = gamma S.

Pressure transforms as P' = gamma^2 P.

Abstract

It is shown that the Lorentz invariant temperature $T^\prime=T$ and entropy $S^\prime=\gamma S$, pressure ${\cal P}^\prime = \gamma^2 {\cal P}$, volume ${\cal V}^\prime ={\cal V}/\gamma$, and energy $U^\prime = \gamma U$, where $\gamma = (1-V^2/c^2)^{-1/2}$, are the correct transformational properties of the thermodynamical quantities of the relativistic ideal gas.