which implies kVSC increases as τ c decreases, being opposed to Eq. 9 (under the lossy regime). When the cavity approaches the lossless regime (τ c → ∞), kVSC → 0 so that there will be no cavity modifications. One can observe in Fig. that the kVSC curve (Eq. 19, blue) agrees well with the right-hand side of the HEOM turnover curve, corresponding to the lossless c (cm 1 ) regime where τ c > 500 fs, although a re-scaling factor of 0.5 is multiplied to kVSC . The τ c → ∞ limit has been numerically investigated in Ref. , suggesting that k/k 0 increases as τ c decreases. The τ c → 0 limit has been numerically checked in Ref. , suggesting that k/k 0 increases as τ c increases. Combining the knowledge of Eq. 9 and Eq. 19, we can predict that there will be a turnover behavior for the VSC-modified rate constant. Equivalently speaking, when τ -1 c → 0 (small friction limit), kVSC ∝ τ -1 c , and when τ -1 c → ∞ (large friction limit) k VSC ∝ τ c . The scaling of the VSC rate constant as a function of τ -1 c coincides with the well-known Kramers turnover . As such, one can regard τ -1 c as the friction parameter for the photon-loss environment. A similar crossover phenomenon has also been discovered in spin relaxation kinetics in semiconductors, e.g., the D'yakonov-Perel' mechanism under different momentum scattering rates .