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

## TL;DR

This paper investigates a Hamiltonian model with long-range interactions, revealing negative temperature regimes where ensemble equivalence breaks down, supported by analytical calculations and molecular dynamics simulations.

## Contribution

It demonstrates the existence of negative-temperature regimes and ensemble nonequivalence in a long-range interacting system through combined analytical and numerical methods.

## Key findings

- Negative temperature regime identified
- Ensemble nonequivalence confirmed
- Fluctuation-Dissipation Theorem validated at negative temperatures

## 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.