Physical interpretation of the canonical ensemble for long-range interacting systems in the absence of ensemble equivalence

Abstract

In systems with long-range interactions, since energy is a non-additive quantity, ensemble inequivalence can arise: it is possible that different statistical ensembles lead to different equilibrium descriptions, even in the thermodynamic limit. The microcanonical ensemble should be considered the physically correct equilibrium distribution as long as the system is isolated. The canonical ensemble, on the other hand, can always be defined mathematically, but it is quite natural to wonder to which physical situations it does correspond. We show numerically and, in some cases, analytically, that the equilibrium properties of a generalized Hamiltonian mean-field model in which ensemble inequivalence is present are correctly described by the canonical distribution in (at least) two different scenarios: a) when the system is coupled via local interactions to a large reservoir (even if the reservoir shows, in turn, ensemble inequivalence) and b) when the mean-field interaction between a small part of a system and the rest of it is weakened by some kind of screening.

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Cited by in corpus (6)

• Statistical mechanics of systems with long-range interactions and negative absolute temperature
• Ensemble inequivalence in the Blume-Emery-Griffiths model near a fourth order critical point
• On the fluctuations of the number of atoms in the condensate
• How Geometrical Frustrated Systems Challenge our Notion of Thermodynamics
• Partial equivalence of statistical ensembles in a simple spin model with discontinuous phase transitions
• Geometrically Frustrated Systems which are as Singles Hotter Than in Company