Fluctuation relations for equilibrium states with broken discrete symmetries

TL;DR

This paper derives exact fluctuation relations for equilibrium spin systems with broken discrete symmetries due to an external magnetic field, linking magnetization probabilities and entropies, and applies these to classical spin models.

Contribution

It introduces novel fluctuation relations for equilibrium states with broken symmetries, extending concepts from nonequilibrium physics to classical spin models.

Findings

Derived exact fluctuation relation for magnetization distribution.

Established relation between entropy, coentropy, and magnetization.

Applied relations to Ising and Curie-Weiss models with magnetic fields.

Abstract

Relationships are obtained expressing the breaking of spin-reversal symmetry by an external magnetic field in Gibbsian canonical equilibrium states of spin systems under specific assumptions. These relationships include an exact fluctuation relation for the probability distribution of the magnetization, as well as a relation between the standard thermodynamic entropy, an associated spin-reversed entropy or coentropy, and the product of the average magnetization with the external field, as a non-negative Kullback-Leibler divergence. These symmetry relations are applied to the model of noninteracting spins, the 1D and 2D Ising models, and the Curie-Weiss model, all in an external magnetic field. The results are drawn by analogy with similar relations obtained in the context of nonequilibrium physics.