R . These analytic expressions provide a complete description for the τ c turnover behavior of the VSC rate constant. Particularly, it provides a novel understanding of the physical role of cavity lifetime in VSC-modified chemical dynamics, that τ -1 c can be viewed as a friction parameter based on the Kramers theory . Under the low friction regime (τ -1 c ≪ Ω R ), the reaction rate is limited by photonic excitation (which resembles energy diffusion) and kVSC ∝ τ -1 c , while under the high friction regime (τ -1