Inconsistent thermostatistics and negative absolute temperatures

TL;DR

This paper argues that negative absolute temperatures are artifacts of an inconsistent entropy definition, and using Gibbs' formalism, temperature remains positive even in systems with bounded spectra.

Contribution

It clarifies that negative temperatures result from an inconsistent entropy choice and advocates for Gibbs' entropy as the correct formalism for thermodynamics.

Findings

Negative temperatures are inconsistent with Gibbs' entropy formalism.

Gibbs' entropy maintains positive temperature in bounded spectrum systems.

Critique of arguments claiming negative absolute temperatures.

Abstract

A considerable body of experimental and theoretical work claims the existence of negative absolute temperatures in spin systems and ultra-cold quantum gases. Here, we clarify that such findings can be attributed to the use of a popular yet inconsistent entropy definition, which violates fundamental thermodynamic relations and fails to produce sensible results for simple analytically tractable classical and quantum systems. Within a mathematically consistent thermodynamic formalism, based on an entropy concept originally derived by Gibbs, absolute temperature remains positive even for systems with bounded spectrum. We address spurious arguments against the Gibbs formalism and comment briefly on heat engines with efficiencies greater than one.