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We analyze a new class of time-periodic nonreciprocal dynamics in interactingchaotic classical spin systems, whose equations of motion are conservative(phase-space-volume-preserving) yet possess no symplectic structure. As aresult, the dynamics of the system cannot be derived from any time-dependentHamiltonian. In the high-frequency limit, we find that the magnetizationdynamics features a long-lived metastable plateau, whose duration is controlledby the fourth power of the drive frequency. However, due to the lack of aneffective Hamiltonian, the prethermal state the system evolves into cannot beunderstood within the framework of the canonical ensemble. We propose aHamiltonian extension of the system using auxiliary degrees of freedom, inwhich the original spins constitute an open yet nondissipative subsystem. Thisallows us to perturbatively derive effective equations of motion thatmanifestly display symplecticity breaking at leading order in the inversefrequency. We thus extend the notion of prethermal dynamics, observed in thehigh-frequency limit of periodically-driven systems, to nonreciprocal systems.

Prethermalization in periodically-driven nonreciprocal many-body spin systems