Title: Heating rates under fast periodic driving beyond linear response

Abstract: We provide a simple formula on the heating rate under fast and strong periodic driving in classical and quantum many-body systems. The key idea behind the formula is constructing a time-dependent dressed Hamiltonian by moving to a rotating frame, which is found by the high-frequency expansion of the micromotion operator. It is shown that the driving part of the dressed Hamiltonian is much weaker than that of the original Hamiltonian. Consequently, the heating rate is evaluated by applying the linear response theory to the dressed Hamiltonian, rather than the bare Hamiltonian. Our heating-rate formula agrees with numerical results both for classical and quantum systems.