Luca Cerino &mdash; Universit&agrave; di Roma <i>La Sapienza</i> #
Statistical properties of isolated systems with negative Boltzmann temperatures #
The possibility of having mechanically isolated systems with negative absolute temperatures is one of the 
most fascinating results of statistical mechanics: however such a possibility dramatically depends upon 
the choice of the definition of entropy. In systems with unbounded phase-space, the two common definitions 
of entropy as the logarithm of the phase space volume (Gibbs entropy) or surface (Boltzmann entropy) are 
equivalent in the thermodynamic limit; this equivalence breaks down in some particular systems where the 
Boltzmann definition can lead to temperatures with negative sign. In the recent past, many authors 
affirmed that the Boltzmann definitions of entropy and temperature cannot be accepted since they are not 
consistent with thermodynamics: nonetheless, we want to emphasize that such a temperature gives a very 
strong characterization of the statistical features of the system. We have studied the dynamics of a chain 
of coupled rotators: in this simple system we can show, with direct numerical computations, the 
differences between the situation at positive and negative absolute temperature. In particular, by 
measuring the time averages of some observable quantities, we are able to show the crucial role of the 
Boltzmann temperature in the statistical description of the system.