  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.
