  The nature of the behaviour of an isolated many-body quantum system
periodically driven in time has been an open question since the beginning of
quantum mechanics. After an initial transient, such a system is known to
synchronize with the driving; in contrast to the non-driven case, no
fundamental principle has been proposed for constructing the resulting
non-equilibrium state. Here, we analytically show that, for a class of
integrable systems, the relevant ensemble is constructed by maximizing an
appropriately defined entropy subject to constraints, which we explicitly
identify. This result constitutes a generalisation of the concepts of
equilibrium statistical mechanics to a class of far-from-equilibrium-systems,
up to now mainly accessible using ad-hoc methods.
