Under the condition that Γ ≪ E, the oscillations of the phase of the off-diagonal density matrix elements due to E are much faster than the decay dynamics. This condition is thus the regime where the Ehrenfest+R approach can be applied with guaranteed accuracy. Under this condition, one can approximate the coherence as ρ 01 ≈ |ρ 01 |e iEt , thus Im[ρ 01 ] 2 ≈ |ρ 01 | 2 sin 2 (Et), which can be used to get an approximate expression of Eq. A13.