Phase transitions at high energy vindicate negative microcanonical temperature

TL;DR

This paper demonstrates that Boltzmann's microcanonical entropy accurately describes negative temperatures and phase transitions at high energy densities, challenging the Gibbs entropy perspective and applying to optical and ultracold lattice systems.

Contribution

It provides analytical and numerical evidence supporting Boltzmann microcanonical entropy as a consistent thermodynamic framework for negative temperatures and phase transitions.

Findings

Boltzmann entropy describes negative temperatures.

Phase transitions occur at high energy densities.

Negative temperature states are observable in optical lattices.

Abstract

The notion of negative absolute temperature emerges naturally from Boltzmann's definition of "surface" microcanonical entropy in isolated systems with a bounded energy density. Recently, the well-posedness of such construct has been challenged, on account that only the Gibbs "volume" entropy ---and the strictly positive temperature thereof--- would give rise to a consistent thermodynamics. Here we present analytical and numerical evidence that Boltzmann microcanonical entropy provides a consistent thermometry for both signs of the temperature. In particular, we show that Boltzmann (negative) temperature allows the description of phase transitions occurring at high energy densities, at variance with Gibbs temperature. Our results apply to nonlinear lattice models standardly employed to describe the propagation of light in arrays of coupled waveguides and the dynamics of ultracold gases trapped in optical lattices. Optically induced photonic lattices, characterized by saturable nonlinearity, are particularly appealing because they offer the possibility of observing states ---and phase transitions--- at both signs of the temperature.