  The dynamical behavior of interacting systems plays a fundamental role for
determining quantum correlations, such as entanglement. In this Letter, we
describe temporal quantum effects of the inseparable evolution of composite
quantum states by comparing the trajectories to their classically correlated
counterparts. For this reason, we introduce equations of motions describing the
separable propagation of any interacting quantum system, which are derived by
requiring separability for all times. The resulting Schroedinger-type equations
allow for comparing the trajectories in a separable configuration with the
actual behavior of the system and, thereby, identifying inseparable and
time-dependent quantum properties. As an example, we study bipartite discrete-
and continuous-variable interacting systems. The generalization of our
developed technique to multipartite scenarios is also provided.
