Consistent thermostatistics forbids negative absolute temperatures

This is a paper written by Jörn Dunkel & Stefan Hilbert in 2013 which criticizes the usage of the so-called “negative temperature” states and suggest that the Gibbs entropy is the only reasonable (consistent) candidate for the statistical counterpart of the thermodynamical entropy. They show that this entropy, while equivalent to Boltzmann entropy at thermodynamic limit, forbids the presence of negative temperature states.

I’ve read this paper because i’ve always thought (and currently thinking!) that statistical mechanics is deeper than it appears (in standard courses) and is not investigated thoroughly as deserved (in contrast to, perhaps, QM, QFT, etc.).