Statistical relativistic temperature transformation for ideal gas of bradyons, luxons and tachyons

TL;DR

This paper derives relativistic temperature and pressure transformations for an ideal gas of bradyons, luxons, and tachyons using a microcanonical statistical approach, confirming consistency with thermodynamic laws and Lorentz invariance.

Contribution

It introduces a unified relativistic temperature transformation applicable to different particle types, aligning with Ott's transformation and thermodynamic principles.

Findings

Temperature transformation matches Ott's formulation.

Thermodynamic $dS$ element is Lorentz-invariant.

Transformations are consistent with thermodynamic laws.

Abstract

Starting from a microcanonical statistical approach and special relativity, the relativistic transformations for temperature and pressure for an ideal gas of bradyons, luxons or tachyons is found. These transformations are in agreement with the three laws of thermodynamic and our temperature transformation is the same as Ott's. Besides, it is shown that the thermodynamic $dS$ element is Lorentz-invariant.