2015/06/30 by P. Buonsante, Pierfrancesco Buonsante, Roberto Franzosi +1 · 25 citations
Computer Science · Mathematics · Physics and Astronomy · #Advanced Fiber Laser Technologies #Boltzmann constant #Bounded function #Canonical ensemble #Entropy (arrow of time) #Mathematics #Microcanonical ensemble #Monte Carlo method #Nonlinear Dynamics and Pattern Formation #Nonlinear Photonic Systems #Nonlinear system #Phase transition #Physics #Quantum mechanics #Statistical physics #Thermodynamics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.95.052135
published in Physical review. E 95(5), 052135 (American Physical Society) · 14 pages, 8 figures. Expanded some concepts. Added one figure in the Appendix and some new references
arxiv created 2015/08/15 · openalex publication_date 2017/05/22 · arxiv updated 2017/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 wave guides 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.