Fluctuation theorems and the generalized Gibbs ensemble in integrable systems

We derive fluctuation relations for a many-body quantum system prepared in a generalized Gibbs ensemble subject to a general nonequilibrium protocol. By considering isolated integrable systems, we find generalizations to the Tasaki-Crooks and Jarzynski relations. Our approach is illustrated by studying the one-dimensional quantum Ising model subject to a sudden change in the transverse field, where we find that the statistics of the work done and irreversible entropy show signatures of quantum criticality. We discuss these fluctuation relations in the context of thermalization.