An absolutely stable open time crystal

Periodically driven (Floquet) systems can host a discrete time crystal (DTC) --- a phase of matter characterized by the spontaneous breaking of time translation symmetry. Time crystalline order with an infinite auto-correlation time relies upon the Floquet system's ability to avoid ergodicity; in particular, it must skirt the absorption of energy from the drive, which would otherwise lead to an infinite temperature final state. In quantum systems, this can be accomplished via strong disorder leading to many-body localization. In this talk, I will describe an entirely different setting where the DTC is stable: locally-interacting, disorder-free, Floquet Hamiltonian dynamics coupled to a finite temperature Langevin bath. Employing a mapping from probabilistic cellular automata to open classical dynamics, the resulting DTC is stable to arbitrary perturbations, including those that break the underlying time translation symmetry of the drive. Finally, I will discuss how general results in the context of probabilistic cellular automata imply the existence of discrete time crystals in all dimensions, D≥1.