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\section{Second-order kinetic model with dynamical disorder}  The effects of dynamic disorder on higher ordered kinetics can be investigated through We adapt  the Kohlrausch-Williams-Watts (KWW) model. This expression takes model for stretched exponential decay to study  the expotential effect of dynamical disorder on higher-order kinetics. In first-order kinetics, stretched exponential  decay predicted by classical kinetics involves a two-parameter survival function  and stretches the curve through associated time-depedent rate coefficient. The parameters are  a time depedent characteristic  rate coefficient $\omega$ or inverse timescale, $\omega$,  andthe coopertavity of decay  $\beta$, making it a conventient expression for interpreting which controls the degree  dynamic disorder.The use of this model is intended to be a proof of principle, however any system with a time depedent rate coefficient may be analyzed.  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 the time derivitive of the inverse of the survival function the time depedent rate coefficient characterising the deacy is expressed as $k(t)=\frac{\beta([A_0]\omega t)^{\beta}}{t}$. We see this definition of the rate coefficient maintains a depedence on the initial concentration of the reactants which is a unique result when compared to first order kinetics, and propagates thorugh the remainder of the calculations.Next calculations. Next  the time depedent rate coefficient is integrated to determine the statistical length. \begin{equation}  \mathcal{L}_{KWW}(\Delta{t})=[A_0\omega t]^{\beta}\bigg|_{t_i}^{t_f}  \end{equation}  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}  \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 \mathcal{J}_{KWW}(\Delta{t}) = \Delta  t [A_0]\beta^2\omega^{2\beta} \ln(t)\bigg|_{t_i}^{t_f} \end{equation}  We use of this model is intended to be a proof of principle, however any system with a time depedent rate coefficient may be analyzed.