where L Ĥ [ρ] propagates the reduced density matrix dynamics corresponding to the system Hamiltonian Ĥ (Eq. 8). The dynamics governed by L Ĥ [ρ], which includes the quantum subsystem, as well as interactions with non-Markovian phonons, can be simulated using PLDM using Eq. 9 and the corresponding EOMs in Eq. 13. The dissipator L L accounts for the cavity loss channel causing the system to relax