Out-of-equilibrium statistical ensemble inequivalence

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 entropy 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 embrace equilibrium as well as out-of-equilibrium regimes.