  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.
