Jarzynski equality for spin glasses and its application

We study an application of Jarzynski equality 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 can be used to derive a lower bound on the performed work during the nonequilibrium process by changing the external magnetic field as well as a pseudo work done during changing temperature. The latter case serves as useful information to implement the population annealing developed in numerical use of the Jarzynski equality to equilibrate the many-body system. We also prove several exact identities that relate equilibrium and nonequilibrium quantities. These identities show possibility of the population annealing to evaluate equilibrium quantities from nonequilibrium computations, which may be useful for avoiding the problem of slow relaxation in spin glasses.