Statistical Mechanics of Systems with Negative Temperature

TL;DR

This paper reviews the concept of negative absolute temperatures in statistical physics, demonstrating their consistency with thermodynamic principles and expanding the understanding of equilibrium and non-equilibrium states.

Contribution

It provides a comprehensive analysis showing that negative temperatures are valid thermodynamic states, challenging previous skepticism and broadening the scope of statistical mechanics.

Findings

Negative temperatures are consistent with equilibrium thermodynamics.

Negative temperature states can be incorporated into thermodynamic frameworks.

The review clarifies misconceptions about negative temperatures as transient phenomena.

Abstract

Do negative absolute temperatures matter 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 review these examples and discuss their peculiar thermodynamic properties, which have been associated to the presence of thermodynamic regimes, characterized by negative absolute temperatures. As reported in this review, the ambiguity inherent the definition of entropy has recurrently raised a harsh debate about the possibility of considering negative temperature states as genuine thermodynamic equilibrium ones. Here we show that negative absolute temperatures are consistent with equilibrium as well as with non-equilibrium thermodynamics. In particular, thermometry, thermodynamics of cyclic transformations, ensemble equivalence, fluctuation-dissipation relations, response theory and even transport processes can be reformulated to include them, thus dissipating any prejudice about their exceptionality, typically presumed as a manifestation of transient metastable effects.