Inverse Temperature 4-vector in Special Relativity

TL;DR

This paper argues that the inverse temperature 4-vector is the only thermodynamically consistent choice in special relativity, emphasizing its future-directed timelike nature and exploring its orientation through a superfluidity thought experiment.

Contribution

It establishes the inverse temperature 4-vector as the unique thermodynamic quantity consistent with the laws of thermodynamics in special relativity and discusses its possible orientations.

Findings

Inverse temperature 4-vector must be future-directed and timelike.

Superfluidity thought experiment shows $f eta$ is not always aligned with the system's time direction.

Entropy-maximum principle may determine the 4-vector for isolated systems.

Abstract

There exist several prescriptions for identifying the notion of temperature in special relativity. We argue that the inverse temperature 4-vector $\bf \beta$ is the only viable option from the laws of thermodynamics, and $\bf \beta$ is a future-directed timelike 4-vector. Using a superfluidity thought experiment, one can show that $\bf \beta$ is not necessarily along the time direction of the comoving frame of the system, as is usually thought. It is conjectured that, for an isolated system, the 4-vector is determined from the entropy-maximum principle.