Isometric fluctuation relations for equilibrium states with broken symmetry

Abstract

We derive a set of isometric fluctuation relations, which constrain the order parameter fluctuations in finite-size systems at equilibrium and in the presence of a broken symmetry. These relations are exact and should apply generally to many condensed-matter physics systems. Here, we establish these relations for magnetic systems and nematic liquid crystals in a symmetry-breaking external field, and we illustrate them on the Curie-Weiss and the $XY$ models. Our relations also have implications for spontaneous symmetry breaking, which are discussed.

9 pages, 4 figures, in press for Phys. Rev. Lett. to appear there in Dec. 2014

References in corpus (3)

• The large deviation approach to statistical mechanics
• Symmetries in Fluctuations Far from Equilibrium
• Energy versus information based estimations of dissipation using a pair of magnetic colloidal particles

Cited by in corpus (6)

• Multiple-scale stochastic processes: decimation, averaging and beyond
• Variance of fluctuations from Noether invariance
• Thermodynamic bounds on equilibrium fluctuations of a global or local order parameter
• Isometric Uncertainty Relations
• Structure of the optimal path to a fluctuation
• Fluctuation Relations associated to an arbitrary bijection in path space