  We investigate quantum effects in the evolution of general systems. For
studying such temporal quantum phenomena, it is paramount to have a rigorous
concept and profound understanding of the classical dynamics in such a system
in the first place. For this reason, we derive from first principles equations
of motions that describe the classical propagation in quantum systems. A
comparison of this classical model with the actual temporal quantum behavior
enables us to identify quantum phenomena in the system's dynamics and
distinguish them from static quantum features at individual points in time. For
instance, we show how Newton's second law emerges as a special case of our
general treatment, connecting it to a Schr\"odinger-type equation. As
applications of our universal technique, we analyze nonlinear optical
processes, semiclassical models, and the multipartite entanglement dynamics of
macroscopic ensembles.
