Pierfrancesco Buonsante — QSTAR Center & INO-CNR Firenze # 
Negative absolute temperatures vindicated # 

Negative absolute temperatures emerge naturally from Boltzmann's definition of "surface" 
microcanonical entropy in isolated systems with a bounded energy density. Recently, the well-posedness of 
negative absolute temperatures has been challenged, on account that only Gibbs "volume" entropy —and the 
strictly positive temperature thereof&mdash; would give rise to a consistent thermodynamics.<br/>

Here we focus on a discrete nonlinear model characterized by bounded energy densities, describing the 
propagation of light in arrays of coupled waveguides. 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 are relevant also to 
ultracold gases trapped in optical lattices.