Gibbs, Boltzmann, and negative temperatures
Abstract
In a recent paper, Dunkel and Hilbert [Nat. Phys. 10, 6772 (2014)] use an entropy definition due to Gibbs to provide a "consistent thermostatistics" that forbids negative absolute temperatures. Here, we argue that the Gibbs entropy fails to satisfy a basic requirement of thermodynamics, namely, that when two bodies are in thermal equilibrium, they should be at the same temperature. The entropy definition due to Boltzmann does meet this test, and moreover, in the thermodynamic limit can be shown to satisfy Dunkel and Hilbert's consistency criterion. Thus, far from being forbidden, negative temperatures are inevitable, in systems with bounded energy spectra.
 Publication:

American Journal of Physics
 Pub Date:
 February 2015
 DOI:
 10.1119/1.4895828
 arXiv:
 arXiv:1403.4299
 Bibcode:
 2015AmJPh..83..163F
 Keywords:

 Condensed Matter  Statistical Mechanics
 EPrint:
 9 pages, 3 figures, RevTeX 4.1  conditionally accepted Am J Phys, with minor changes from previous version