Nonequilibrium relations for spin glasses with gauge symmetry

We study the applications of nonequilibrium 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 nonequilibrium process of temperature change. We also prove identities that relate equilibrium and nonequilibrium quantities. These identities suggest a method of evaluating equilibrium quantities from nonequilibrium computations, which may be useful for avoiding the problem of slow relaxation in spin glasses.