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\section{Second-order kinetic model with dynamical disorder}  We adapt the Kohlrausch-Williams-Watts (KWW) model for stretched exponential decay to study the effect of dynamical disorder on higher-order kinetics. In first-order kinetics, stretched exponential decay involves a two-parameter survival function $\exp(-\omega t)^\beta$  and associated time-depedent rate coefficient. coefficient, $k_{1,KWW}(t) = \beta(\omega t)^{\beta}/t$.  The parameters are a characteristic rate or inverse timescale, $\omega$, and $\beta$, which controls the degree dynamic disorder. Assuming an overall second order process with a time depedent rate coefficient the survival function is written as $S(t)=\frac{1}{1+(\omega t[A_0])^{\beta}}$.Thorugh $S_2(t) = 1/\left(1+(\omega tC_A(0))^{\beta}\right)$. Through  the time derivitive time-derivative  of the inverse of the survival function the time depedent rate coefficient characterising characterizing  the deacy decay  is expressed as $k(t)=\frac{\beta([A_0]\omega t)^{\beta}}{t}$. $k_{2,KWW}(t) = \beta(C_A(0)\omega t)^{\beta}/t$.  We see this definition of the rate coefficient maintains a depedence dependence  on the initial concentration of the reactants which is a unique result when compared comapared  tofirst order kinetics, and propagates thorugh the remainder of  the calculations. Next first-order result. Integrating  the time depedent time-depedent  rate coefficient is integrated to determine gives  the statistical length. length  \begin{equation}  \mathcal{L}_{KWW}(\Delta{t})=[A_0\omega t]^{\beta}\bigg|_{t_i}^{t_f} \mathcal{L}_{KWW}(\Delta{t}) = \left(C_A(0)\omega t\right)^{\beta}\big|_{t_i}^{t_f}  \end{equation}  which also has a concentration dependence to cancel the concentration dimensions of the $\omega$.  To understand the effect of fluctuations on the rate coefficient we then integrate over the square, determining the divergence. \begin{equation}  \mathcal{J}_{KWW}(\Delta{t}) =  \frac{\Delta t[A_0]^{2\beta}\beta^{2}\omega^{2\beta}t^{2\beta-1}}{2\beta-1}\bigg|_{t_i}^{t_f} tC_A(0)^{2\beta}\beta^{2}\omega^{2\beta}t^{2\beta-1}}{2\beta-1}\bigg|_{t_i}^{t_f}  \end{equation}  This form shows the $\frac{1}{2}$ $\beta$ valuse must be evaluated seperately which yields the final result for comparison. And when $\beta=\frac{1}{2}$,  \begin{equation}  \mathcal{J}_{KWW}(\Delta{t}) = \Delta t [A_0]\beta^2\omega^{2\beta} \ln(t)\bigg|_{t_i}^{t_f} C_A(0)\beta^2\omega^{2\beta} \ln(t)\big|_{t_i}^{t_f}  \end{equation}  We use of this model is intended to be as  a proof of principle, however any system with model  a time depedent time-depedent  rate coefficient may can  be analyzed. subject to this analysis.