A note on the relativistic temperature

TL;DR

This paper critically examines existing relativistic temperature transformations, demonstrating their failure to satisfy the closure property, and proposes alternative transformations consistent with special relativity principles.

Contribution

It introduces new relativistic temperature transformations that satisfy the closure property, aligning with the velocity addition law of special relativity.

Findings

Existing transformations do not satisfy the closure property.

Proposed transformations are consistent with special relativity.

They can be interpreted as specific cases of directional temperature.

Abstract

We show that the largely debated Planck-Einstein and Ott-Arzelies relativistic transformations of temperature do not satisfy the closure group property that two successive temperature transformations must be equivalent to a single temperature transformation of the same form with the involved reference frame velocities satisfying the velocity addition law of special relativity. We then suggest relativistic transformations of temperature that do satisfy this closure requirement and argue that they may be interpreted as particular cases of the so-called directional temperature.