Out of equilibrium statistical ensemble inequivalence

TL;DR

This paper investigates how an external magnetic field induces ensemble inequivalence in a one-dimensional rotator model, revealing negative susceptibility and negative temperature states, highlighting non-Boltzmannian out-of-equilibrium phenomena.

Contribution

It demonstrates the emergence of ensemble inequivalence driven by an external magnetic field in a mean-field rotator model, with analytical and simulation validation, and explores non-standard thermodynamic behaviors.

Findings

Negative microcanonical magnetic susceptibility observed.

Negative temperature states identified.

Ensemble inequivalence linked to non-convex energy regions.

Abstract

We consider a paradigmatic model describing the one-dimensional motion of $N$ rotators coupled through a mean-field interaction, and subject to the perturbation of an external magnetic field. The latter is shown to significantly alter the system behaviour, driving the emergence of ensemble inequivalence in the out-of-equilibrium phase, as signalled by a negative (microcanonical) magnetic susceptibility. The thermodynamic of the system is analytically discussed, building on a maximum entropy scheme justified from first principles. Simulations confirm the adequacy of the theoretical picture. Ensemble inequivalence is shown to rely on a peculiar phenomenon, different from the one observed in previous works. As a result, the existence of a convex intruder in the micro-canonical energy is found to be a necessary but not sufficient condition for inequivalence to be (macroscopically) observed. Negative temperature states are also found to occur. These intriguing phenomena reflect the non-Boltzmanian nature of the scrutinized problem and, as such, bear traits of universality that embraces equilibrium as well out-of-equilibrium regimes.