Related Experiment Video
Updated: Oct 2, 2025

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Equilibrium and nonequilibrium description of negative temperature states in a one-dimensional lattice using a wave
M Onorato1,2, G Dematteis3, D Proment4
1Dipartimento di Fisica, Università degli Studi di Torino, 10125 Torino, Italy.
Abstract:
We predict negative temperature states in the discrete nonlinear Schödinger (DNLS) equation as exact solutions of the associated wave kinetic equation. Within the wave kinetic approach, we define an entropy that results monotonic in time and reaches a stationary state, that is consistent with classical equilibrium statistical mechanics. We also perform a detailed analysis of the fluctuations of the actions at fixed wave numbers around their mean values. We give evidence that such fluctuations relax to their equilibrium behavior on a shorter timescale than the one needed for the spectrum to reach the equilibrium state. Numerical simulations of the DNLS equation are shown to be in agreement with our theoretical results. The key ingredient for observing negative temperatures in lattices characterized by two invariants is the boundedness of the dispersion relation.
Related Concept Videos
Zeroth Law of Thermodynamics
Atomic Nuclei: Nuclear Spin State Population Distribution
The de Broglie Wavelength
First Law: Particles in One-dimensional Equilibrium
Third Law of Thermodynamics
Trends in Lattice Energy: Ion Size and Charge

