Statistical mechanics of systems with long-range interactions and negative absolute temperature

Abstract

A Hamiltonian model living in a bounded phase space and with long-range interactions is studied. It is shown, by analytical computations, that there exists an energy interval in which the microcanonical entropy is a decreasing convex function of the total energy, meaning that ensemble equivalence is violated in a negative-temperature regime. The equilibrium properties of the model are then investigated by molecular dynamics simulations: first, the caloric curve is reconstructed for the microcanonical ensemble and compared to the analytical prediction, and a generalized Maxwell-Boltzmann distribution for the momenta is observed; then, the nonequivalence between the microcanonical and canonical descriptions is explicitly shown. Moreover, the validity of Fluctuation-Dissipation Theorem is verified through a numerical study, also at negative temperature and in the region where the two ensembles are nonequivalent.

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Cited by in corpus (6)

• Statistical Mechanics of Systems with Negative Temperature
• On the Fluctuation-Dissipation Relation in non-equilibrium and non-Hamiltonian systems
• Localization transition in the Discrete Non-Linear Schrödinger Equation: ensembles inequivalence and negative temperatures
• Negative-temperature Fourier transport in one-dimensional systems
• Geometrically Frustrated Systems which are as Singles Hotter Than in Company
• Effective Equations in complex systems: from Langevin to machine learning