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A time correlation $C_{fs}(t)=⟨\delta (s_0){\dot{s}}_0\Theta (s_t)⟩$ correlating signed initial flux through a dividing surface with product-side occupation at a later time. Dividing by reactant population gives a rate on a plateau after microscopic recrossing and before macroscopic equilibration.

Put the dividing surface at $x^{‡}<0$. The immediate positive flux includes all positive momenta and gives $C_{fs}(0^{+})=1/(2\pi \hslash \beta )$, an overestimate. Trajectories with $p^2/(2m)<V_0$ hit the barrier, return across this surface, and cease contributing to the later product-side indicator. After their recrossing transient, only $p>\sqrt{2m{V}_0}$ survives:The exact rate is again unchanged; the transmission correction to the reactant-side transition-state estimate is $e^{-\beta V_0}$. The return time depends on surface placement and velocity, so the plateau means a timescale-separated limiting flux, not the claim that every trajectory has one identical finite recrossing time.

Choose a reaction coordinate $s(q)$ that is negative in the reactant region and positive in the product region; $s=0$ defines a dividing surface. With unnormalized canonical phase-space averaging, defineThe signed initial flux $\delta (s)\dot{s}$ counts both directions, while the later side function tests product commitment. The rate is $k=C_{fs}(t_{\mathrm{pl}})/Q_r$ on a plateau after microscopic recrossings have died away but before reactant depletion and global equilibration become important. The $t\to 0^{+}$ limit instead gives the transition-state-theory positive flux and can overcount trajectories that later return. A suitable dividing surface changes that early flux but not a correctly evaluated committed plateau rate. This correlation formulation provides the dynamical correction to a transition-state estimate.^[ref]