Long-time properties of generic Floquet systems are approximately periodic with the driving period

A Floquet quantum system is governed by a Hamiltonian that is periodic in time. Consider the space of piecewise time-independent Floquet systems with (geometrically) local interactions. We prove that for all but a measure zero set of systems in this space, starting from a random product state, many properties (including expectation values of observables and the entanglement entropy of a macroscopically large subsystem) at long times are approximately periodic with the same period as the Hamiltonian. Thus, in almost every Floquet system of arbitrarily large but finite size, discrete time-crystalline behavior does not persist to strictly infinite time.