where χ eq ≡ P R /P P denotes the ratio of equilibrium population between the reactant and product. For the symmetric double potential model considered in this work, χ eq = 1. The limit t → t p represents that the dynamics have already entered the rate process regime (linear response regime) and t p represents the "plateau time" of the time-dependent rate which is equivalent to a flux-side time correlation function formalism . Details of the simulations are provided in Supplementary Note 3.