Is relativistic transformation for thermodynamic quantities possible?

Abstract

For thermodynamic quantities, different relativistic transformations have been suggested by Plank–Einstein, Ott and Landsberg. In this article, relativistic thermodynamics has been discussed using partition function. For the discussion, quantum system of a particle in 3-D box has been considered. All known relativistic transformations are applied to this system to discuss the consistency of thermodynamic quantities in different frames. For this system, the invariance of entropy yields a new temperature and pressure transformations as $T^\prime =T\gamma ^{1/3}$ and $P^\prime =P \gamma ^{-2/3}$, respectively. Though this transformation has been obtained for a single particle system, the validity of this transformation has been tested for mono-atomic gas with spin-less particles and black-body.