On the dispute between Boltzmann and Gibbs entropy

Year: 2016

Authors: Buonsante P., Franzosi R., Smerzi A.

Autors Affiliation: Ist Nazl Ottica, QSTAR, Largo Enrico Fermi 2, I-50125 Florence, Italy; Ist Nazl Ottica, CNR, Largo Enrico Fermi 2, I-50125 Florence, Italy.

Abstract: The validity of the concept of negative temperature has been recently challenged by arguing that the Boltzmann entropy (that allows negative temperatures) is inconsistent from a mathematical and statistical point of view, whereas the Gibbs entropy (that does not admit negative temperatures) provides the correct definition for the microcanonical entropy. Here we prove that the Boltzmann entropy is thermodynamically and mathematically consistent. Analytical results on two systems supporting negative temperatures illustrate the scenario we propose. In addition we numerically study a lattice system to show that negative temperature equilibrium states are accessible and obey standard statistical mechanics prediction. (C) 2016 Elsevier Inc. All rights reserved.

Journal/Review: ANNALS OF PHYSICS

Volume: 375      Pages from: 414  to: 434

KeyWords: Statistical Mechanics, Microcanonical ensemble, Bose Einstein condensation, Photorefractive crystals
DOI: 10.1016/j.aop.2016.10.017

Citations: 43
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