  Discrete time crystals (DTCs) are a many-body state of matter whose dynamics
are slower than the forces acting on it. The same is true for classical systems
with period-doubling bifurcations. Hence, the question naturally arises what
differentiates classical from quantum DTCs. Here, we analyze a variant of the
Bose-Hubbard model, which describes a plethora of physical phenomena and has
both a classical and a quantum time-crystalline limit. We study the role of
fluctuations on the stability of the system and find no distinction between
quantum and classical DTCs. This allows us to probe the fluctuations in an
experiment using two strongly coupled parametric resonators subject to
classical noise.
