Can one measure negative specific heat in the canonical statistical ensemble?

TL;DR

This paper challenges the conventional belief that negative specific heat cannot be observed in the canonical ensemble, showing it can occur in non-Boltzmannian or out-of-equilibrium systems.

Contribution

It demonstrates that negative specific heat can be measured in the canonical ensemble under certain non-Boltzmannian or out-of-equilibrium conditions.

Findings

Negative specific heat can occur in the canonical ensemble.

Non-Boltzmannian systems can exhibit negative specific heat.

Out-of-equilibrium systems may display negative specific heat in the canonical ensemble.

Abstract

According to thermodynamics, the specific heat of Boltzmannian short-range interacting systems is a positive quantity. Less intuitive properties are instead displayed by systems characterized by long-range interactions. In that case, the sign of specific heat depends on the considered statistical ensemble: negative specific heat can be found in isolated systems, which are studied in the framework of the microcanonical ensemble; on the other hand, it is generally recognized that a positive specific heat should always be measured in systems in contact with a thermal bath, for which the canonical ensemble is the appropriate one. We demonstrate that the latter assumption is not generally true: one can in principle measure negative specific heat also in the canonical ensemble if the system under scrutiny is non-Boltzmannian and/or out-of-equilibrium.