  We show that periodically driven superconducting vortices in the presence of
quenched disorder exhibit a transition from reversible to irreversible flow
under increasing vortex density or cycle period. This type of behavior has
recently been observed for periodically sheared colloidal suspensions and we
demonstrate that driven vortex systems exhibit remarkably similar behavior. We
also provide evidence that the onset of irreversible behavior is a dynamical
phase transition.
