Phase transitions at high energy vindicate negative microcanonical temperature

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.

14 pages, 8 figures. Expanded some concepts. Added one figure in the Appendix and some new references

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Cited by in corpus (17)

• Temperature in and out of equilibrium: a review of concepts, tools and attempts
• Weakly nonergodic dynamics in the Gross--Pitaevskii lattice
• Statistical Mechanics of Systems with Negative Temperature
• Optical Phase Transitions in Photonic Networks: A Spin System Formulation
• Probing band topology using modulational instability
• Fundamental entropic processes in the theory of optical thermodynamics
• Non-Gibbs states on a Bose-Hubbard lattice
• Topological Theory of Phase Transitions
• Geometrical aspects in the analysis of microcanonical phase-transitions
• Microcanonical entropy for classical systems
• Critique of the Gibbs volume entropy and its implication
• Thermalization in the one-dimensional Salerno model lattice
• A microcanonical entropy correcting finite-size effects in small systems
• Entanglement estimation in non-optimal qubit states
• Coarse-graining and symplectic non-squeezing
• Temperature fluctuations in finite systems: Application to the one-dimensional Ising chain
• Thermalization in a nonlinear variant of the discrete nonlinear Schrödinger Equation