  We demonstrate that the prethermal regime of periodically driven (Floquet),
classical many-body systems can host nonequilibrium phases of matter. In
particular, we show that there exists an effective Hamiltonian that captures
the dynamics of ensembles of classical trajectories despite the breakdown of
this description at the single trajectory level. In addition, we prove that the
effective Hamiltonian can host emergent symmetries protected by the discrete
time-translation symmetry of the drive. The spontaneous breaking of such an
emergent symmetry leads to a subharmonic response, characteristic of time
crystalline order, that survives to exponentially late times in the frequency
of the drive. To this end, we numerically demonstrate the existence of
classical prethermal time crystals in systems with different dimensionalities
and ranges of interaction. Extensions to higher order and fractional time
crystals are also discussed.
