The discrepancy between the dynamics obtained from the L-MFE method and the exact Lindblad dynamics is due to the inadequacy of MFE as a mixed quantumclassical method. This demonstrates the need to incorporate Lindblad dynamics into more accurate mixed quantum-classical or semiclassical approaches that go beyond the approximations present in the mean-field Ehrenfest approach. Note that in recent investigations of molecular cavity quantum electrodynamics, the photonic population decay is incorporated in a similar fashion as described in Eq. 69a-69c. However, in these early investigations, the random phase e iθ ξ (in Eq. 69b) is not incorporated. We have demonstrated the consequence of missing this random phase in Fig. , where artificial coherences are generated. Future wavefunction based investigations in molecular cavity QED should carefully describe the decay dynamics using the approach outlined in L-MFE.