Fluctuation theorems on the Nishimori line

The distribution of the performed work for spin glasses with gauge symmetry is considered. With the aid of gauge symmetry, which leads to exact (rigorous) results in spin glasses, we find a fascinating relation of the performed work to the fluctuation theorem. The integral form of the resultant relation reproduces the Jarzynski-type equation for spin glasses that we have obtained. We show that similar relations can be established not only for the distribution of the performed work but also for that of the free energy of spin glasses with gauge symmetry, which provides another interpretation of the phase transition in spin glasses.