The current analytic theory kVSC (Eq. 17) also explains why under the lossless regime (Ω R ≫ τ -1 c ), the rate constant increase when decreasing the cavity lifetime τ c (see Eq. , agreeing with the previous numerically exact simulations . Under the lossy regime (Ω R ≪ τ -1 c ), our previous work provides an analytic theory k VSC (Eq. 2), which predicts that the rate constant will increase as τ c increases (see Eq. 9). Both k VSC and kVSC agree well with the numerical exact HEOM results under their specific regimes. The combination of kVSC (Eq. 17) and k VSC (Eq. 2) provides a complete picture of the τ cdependence of the VSC rate constant modification and suggests there should be a turnover behavior. The physical picture of the cavity enhancement effect for the rate constant is clarified by the reaction mechanisms in Eq. 1 (limited by vibrational excitation) under the lossy regime and Eq. 11 (limited by photonic excitation) under the lossless regime. The cavity loss parameter τ -1 c can thus be viewed as a friction parameter associated with the cavity mode qc and the turnover behavior of the rate constant is essentially the Kramers turnover. We also provided an interpolating scheme (Eq. 20) for the description of the turnover phenomenon and predicted that the maximal enhancement will be reached when τ c = Ω -1 R (see Eq. 21), all agree well with the exact simulations.