  The applications of nonequilbrium relations such as the Jarzynski equality
and the fluctuation theorem to spin glasses are considered. The spin glass is a
basic platform where we consider an application of an approximate solver of
combinatorial optimization problems, simulated annealing. We find a novel
relationship between an average through a nonequilibrium process where the
temperature changes as in simulated annealing and a thermal average in
equilibrium with different amounts of quenched randomness. The results shown in
the present study may serve as an alternative way to overcome critical slowing
down in spin glasses. It means that this way may mitigate difficulties in
several hard optimization problems.
