Fig. presents k/k 0 as a function of cavity frequency ω c with different cavity lifetime τ c (colorcoded with the legend in panel (a)), obtained from (a) the numerically exact HEOM simulation and (b) γ-SQC simulations. The light-matter coupling strength is η c = 1.25 × 10 -3 a.u., and the cavity lifetime is varied from 100 fs to 10000 fs. We can see the VSC-enhancement of the k/k 0 increase first, from τ c = 100 fs (black dashed lines) to τ c = 200 fs (red solid line), then gradually decay by further increasing the cavity lifetime to τ c = 500 fs and more. This rate constant turnover was discovered in our previous work, and here, we demonstrate that γ-SQC (and in fact all MQC methods explored here) can semi-quantitatively reproduce the same trend. The analytic theory in Eq. 8 can not describe such a turnover of k/k 0 as a function of τ c , and future analytic work is required to develop a theory that is capable of describing this behavior.