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…
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