where the initial vibrational excitation (|ν L ⟩ → |ν ′ L ⟩) is the rate-limiting step, such that k 1 ≪ k 2 , k 3 , see Fig. . This will lead to a steady state population (time-independent plateau population) of the intermediate states |ν ′ L ⟩ and |ν ′ R ⟩, and the overall rate constant for the entire reaction (k) can be approximate as k ≈ k 1 . The |ν L ⟩ → |ν ′ L ⟩ transition is influenced by the energy exchange between the phonon bath and the RPV modes {Q j }. When resonantly coupled to the cavity, the lightmatter hybrid system has a set of polaritonic modes with frequencies ω ± = ω Q ± Ω R /2, thus effectively removing the RPV's from the |ν L ⟩ → |ν ′ L ⟩ transition, explicitly changing the value of k 1 , and as |ν L ⟩ → |ν ′ L ⟩ is still the rate-limiting step for system compiled inside the cavity (see Supplementary Note 4), the influence of cavity on k 1 explicitly shows up in the entire apparent rate constant of the reaction.