At the same time, the quantum subsystem, in principle, can also interact with other environmental DOFs. Example of these interacting environmental DOFs include the interaction of the electromagnetic field with molecules that causes spontaneous emission and farfield electromagnetic modes that couple to a quantized radiation mode inside an optical cavity that causes phoa) Electronic mail: ekoessle@ur.rochester.edu b) Electronic mail: pengfei.huo@rochester.edu ton leakage. It is often desirable to implicitly capture the environmental influence on the dynamics and avoid simulating these environmental DOFs explicitly. Another example is the presence of high frequency vibrations in molecules that are essentially Markovian for the subsystem dynamics. These high frequency vibrations, however, cause difficulties for MQC simulations due to the inadequate description of them using classical trajectories. A number of approaches seek to phenomenologically incorporate these effects of population decay from a higher energy state to a lower energy state through an imaginary Hamiltonian approach, incorporating ad-hoc first-order decay processes, or a posteriori probabilistic collapse into the ground state. These approaches do not capture the full nature of the decay dynamics as they generally do not describe the dynamics of the ground state at the wavefunction level, or do not account for proper decoherence processes during the population decay dynamics.