Nonequilibrium work on spin glasses in longitudinal and transverse fields

TL;DR

This paper derives exact relations between equilibrium and nonequilibrium properties of spin glasses in external fields, using the Jarzynski equality and gauge symmetry, with implications for quantum annealing.

Contribution

It introduces new identities and bounds linking equilibrium and nonequilibrium quantities in spin glasses, applicable to both classical and quantum annealing processes.

Findings

Established a lower bound for work in nonequilibrium processes with random fields.

Proven identities relating physical quantities and exponentiated work in quantum annealing.

Suggested the Jarzynski equality as a tool for non-adiabatic quantum annealing.

Abstract

We derive a number of exact relations between equilibrium and nonequilibrium quantities for spin glasses in external fields using the Jarzynski equality and gauge symmetry. For randomly-distributed longitudinal fields, a lower bound is established for the work done on the system in nonequilibrium processes, and identities are proven to relate equilibrium and nonequilibrium quantities. In the case of uniform transverse fields, identities are proven between physical quantities and exponentiated work done to the system at different parts of the phase diagram with the context of quantum annealing in mind. Additional relations are given, which relate the exponentiated work in quantum and simulated (classical) annealing. It is also suggested that the Jarzynski equality may serve as a guide to develop a method to perform quantum annealing under non-adiabatic conditions.