# Gibbs volume entropy is incorrect.

@article{Swendsen2015GibbsVE, title={Gibbs volume entropy is incorrect.}, author={Robert H. Swendsen and Jian-Sheng Wang}, journal={Physical review. E, Statistical, nonlinear, and soft matter physics}, year={2015}, volume={92 2}, pages={ 020103 } }

We show that the expression for the equilibrium thermodynamic entropy contains an integral over a surface in phase space, and in so doing, we confirm that negative temperature is a valid thermodynamic concept. This demonstration disproves the claims of several recent papers that the Gibbs entropy, which contains an integral over a volume in phase space, is the correct definition and that thermodynamics cannot be extended to include negative temperatures. We further show that the Gibbs entropy…

## 29 Citations

The question of negative temperatures in thermodynamics and statistical mechanics

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This paper will show that standard thermodynamics, with some minor generalizations, is correct, and the alternative thermodynamics suggested by Hilbert, Hänggi, and Dunkel is not, and that negative temperatures are thermodynamically consistent.

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This paper analyzes and calculates the thermodynamic entropy for large but finite quantum mechanical systems and preserves all required thermodynamic properties, including satisfaction of all postulates and laws of thermodynamics.

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Despite well over a century of effort, the proper expression for the classical entropy in statistical mechanics remains a subject of debate. The Boltzmann entropy (calculated from a surface in phase…

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Dunkel and Hilbert, "Consistent thermostatistics forbids negative absolute temperatures," Nature Physics, {\bf 10}, 67 (2014), and Hilbert, H\"anggi, and Dunkel, "Thermodynamic laws in isolated…

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