Periodic driving of a quantum (or classical) many-body system can alter the systems properties significantly and therefore has emerged as a promising way to engineer exotic quantum phases, such as topological insulators and discrete time crystals. A major limitation in such setups, is that generally interacting, driven systems will heat up over time and lose the desired properties. Understanding the relevant time scales is thus an important topic in the field and so far, there have only been few approaches to determine heating times for a concrete system quantitatively, and in a computationally efficient way. In this article we propose a new approach, based on building the heating rate from microscopic processes, encoded in avoided level crossings of the Floquet propagator. We develop a method able to resolve individual crossings and show how to construct the heating rate based on these. The method is closely related to the Fermi Golden Rule approach for weak drives, but can go beyond it, since it captures non-perturbative effects by construction. This enables our method to be applicable in scenarios such as the heating time of discrete time crystals or frequency dependent couplings, which are very relevant for Floquet engineering, where previously no efficient methods for estimating heating times were available.

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Recently it was demonstrated theoretically and experimentally that the presence of a moving conductor can break the reciprocity in the interactions between magnetic dipoles. In this article we investigate the influence of nonreciprocity on the dynamics of a pair of rigid XY dipoles, which have been realized in experiments. In particular, we focus on the energy nonconservation, which is a consequence of the nonreciprocity. We find that the dynamics indeed has regimes, wherein the kinetic energy grows quadratically. However, whether energy absorption occurs depends strongly on the initial conditions on the dipoles. Simulations for various initial conditions reveal an intricate dependence, resulting in a rich structure of the energy absorbing regime in the initial condition space. Nevertheless, we provide a qualitative explanation of these observations, interpreting the absence of energy absorption as a confinement of the dynamics in phase space.