Notes on thermodynamics in special relativity

TL;DR

This paper examines the foundations of thermodynamics within special relativity, endorsing specific transformation formulas for heat and temperature, supported by statistical and simulation evidence.

Contribution

It clarifies the correct relativistic transformations of thermodynamic quantities and connects phenomenological and statistical approaches.

Findings

Relativistic transformations of heat and temperature follow Ott, Arzeliès, and Möller's formulas.

Relativistic Gibbs distribution for ideal gas is consistent with these transformations.

Computer simulations verify the relativistic Gibbs distribution.

Abstract

Foundations of thermodynamics in special theory of relativity are considered. We argue that from the phenomenological point of view the correct relativistic transformations of heat and absolute temperature are given by the formulae proposed by H. Ott, H. Arzeli\`{e}s and C. M\oller. It is shown that the same transformation rules can be also found from the relativistic Gibbs distribution for ideal gas. This distribution has been recently verified by the computer simulations. Phenomenological and statistical thermometers in relativistic thermodynamics are analysed.