  In a recent paper, Dunkel and Hilbert [Nature Physics 10, 67-72 (2014)] use
an entropy definition due to Gibbs to provide a 'consistent thermostatistics'
which 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.
