In defence of negative temperature

TL;DR

This paper defends the concept of negative temperature, clarifying misconceptions about its thermodynamic validity and consistency within the Boltzmann and Gibbs entropy frameworks.

Contribution

It provides a clear pedagogical argument affirming the thermodynamic legitimacy of negative temperatures and clarifies misconceptions related to entropy definitions.

Findings

Both Boltzmann and Gibbs entropies satisfy thermodynamic relations.

Boltzmann entropy complies with the second law of thermodynamics.

An integrating factor exists for heat differential under both entropy definitions.

Abstract

This pedagogical comment highlights three misconceptions concerning the usefulness of the concept of negative temperature; being derived from the usual, often termed Boltzmann, definition of entropy. First, both the Boltzmann and Gibbs entropies must obey the same thermodynamic consistency relation. Second, the Boltzmann entropy does obey the second law of thermodynamics. Third, there exists an integrating factor of the heat differential with both definitions of entropy.