Non-equilibrium Relations for Spin Glasses with Gauge Symmetry

Abstract

We study the applications of non-equilibrium relations such as the Jarzynski equality and fluctuation theorem to spin glasses with gauge symmetry. It is shown that the exponentiated free-energy difference appearing in the Jarzynski equality reduces to a simple analytic function written explicitly in terms of the initial and final temperatures if the temperature satisfies a certain condition related to gauge symmetry. This result is used to derive a lower bound on the work done during the non-equilibrium process of temperature change. We also prove identities relating equilibrium and non-equilibrium quantities. These identities suggest a method to evaluate equilibrium quantities from non-equilibrium computations, which may be useful to avoid the problem of slow relaxation in spin glasses.

8 pages, 2 figures, submitted to JPSJ

References in corpus (6)

• A nonequilibrium equality for free energy differences
• The Entropy Production Fluctuation Theorem and the Nonequilibrium Work Relation for Free Energy Differences
• Exchange Monte Carlo Method and Application to Spin Glass Simulations
• Equilibrium free energy differences from nonequilibrium measurements: a master equation approach
• Path ensembles averages in systems driven far-from-equilibrium
• Population Monte Carlo algorithms

Cited by in corpus (10)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• Mathematical understanding of detailed balance condition violation and its application to Langevin dynamics
• Nonequilibrium work on spin glasses in longitudinal and transverse fields
• Microcanonical work and fluctuation relations for an open system: An exactly solvable model
• Nonequilibrium work performed in quantum annealing
• Stochastic gradient method with accelerated stochastic dynamics
• Fluctuation Theorems on Nishimori Line
• Nonequilibrium relations in spin glasses
• Proposal of a Checking Parameter in the Simulated Annealing Method Applied to the Spin Glass Model
• Toward mean-field bound for critical temperature on Nishimori line