Statistical mechanics of systems with negative temperature

Abstract

Are negative absolute temperatures relevant physics and specifically Statistical Physics? We provide evidence that we can certainly answer positively to this vexata quaestio. The great majority of models investigated by statistical mechanics over almost one century and a half exhibit positive absolute temperature, because their entropy is a nondecreasing function of energy. Since more than half a century ago it has been realized that this may not be the case for some physical systems as incompressible fluids, nuclear magnetic chains, lasers, cold atoms and optical waveguides. We discuss these examples and their peculiar thermodynamic properties, which have been associated to the presence of thermodynamic regimes, characterized by negative absolute temperatures. The ambiguity regarding the definition of entropy has recurrently raised a harsh debate about the possibility of considering negative temperature states as genuine thermodynamic equilibrium ones. We show that negative absolute temperatures are consistent with equilibrium as well as with non-equilibrium thermodynamics.