Fig. shows the population transfer rates between the two polaritons and the dark states in the zero detuning case ω x = ω c , with N = 5 (dashed lines) and N = 10 6 (solid lines). The Rabi splitting 2 √ N g c is kept invariant. Consistent with previous works on NE-FGR, the timedependent rates converge to the corresponding E-FGR rate after a transient period of time, in this case, ∼ 50 fs. Panel (f) of Fig. shows the E-FGR rates responsible for the dynamics beyond the transient non-equilibrium period, as a function of N . Four E-FGR rates, k D→± and k ±→∓ , decreases as N increases. On the log-log scale, these four E-FGR rates form straight lines with a slope of -1, meaning these rates scale with 1/N . Such scaling comes naturally in the collective limit (N = 10 3 and N = 10 6 , Eq. 30a), but not in the non-collective case (N = 5 and N = 50, Fourier transform of Eqs. 23, 26a) due to the C 0 (t, s) term. The fact that the non-collective rates stay in a straight line with the collective rates means that the C 0 (t, s) term has a minor influence on the rate constants. The remaining two rates, k ±→D , are expected to scale with (N -1)/N , which is close to a horizontal line on the log-log plot, which agrees with panel (f).