Prethermal non-equilibrium phases in classical systems

High-frequency driven quantum systems exhibit long-lived prethermal regimes, where the dynamics are described by effective static Hamiltonians. The existence of such prethermal regime allows exotic non-equilibrium phases to emerge. However, generalizing these phenomena to classical many-body systems remains challenging. In our work, we elucidate the nature of the prethermal regime in classical spin systems. We first demonstrate that the chaotic nature of the classical evolution places an obstacle to define an effective prethermal Hamiltonian: for an initial state, any small error in the dynamics becomes exponentially magnified over time. While such obstacle is inevitable for a single classical trajectory, an effective description can still arise when considering the evolution of an ensemble of states. This then allows us to extend the properties of quantum prethermal dynamics to classical systems. In particular, we prove the existence of an emergent symmetry in the prethermal regime, and utilize this symmetry to generate novel non-equilibrium phases such as classical prethermal discrete time crystals (CPDTC). Finally, we will present an analytical framework as well as numerical demonstration of CPDTC.