Simple spin models with non-concave entropies

Abstract

Two simple spin models are studied to show that the microcanonical entropy can be a non-concave function of the energy, and that the microcanonical and canonical ensembles can give non-equivalent descriptions of the same system in the thermodynamic limit. The two models are simple variations of the classical paramagnetic spin model of non-interacting spins and are solved as easily as the latter model.

v1: 11 pages, 5 figures. v2: Short, published version of v1, 6 pages, 3 figures. See v1 for the solutions of some of the problems listed in v2

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Cited by in corpus (10)

• The large deviation approach to statistical mechanics
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• The thermodynamic limit and black hole entropy in the area ensemble
• A large deviation perspective on ratio observables in reset processes: robustness of rate functions
• Non equivalence of dynamical ensembles and emergent non ergodicity
• Methods for calculating nonconcave entropies
• Density large deviations for multidimensional stochastic hyperbolic conservation laws
• Slow dynamics and subdiffusion in a non-Hamiltonian system with long-range forces
• Specific behavior of one chaotic dynamics near the fine-structure constant