deletions | additions       diff --git a/$n^{th}$ Order Irreversible Decay.tex b/$n^{th}$ Order Irreversible Decay.tex  index b4c8b4b..66ca0da 100644  --- a/$n^{th}$ Order Irreversible Decay.tex  +++ b/$n^{th}$ Order Irreversible Decay.tex 
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\end{equation}  The time dependent rate coefficient is  \begin{equation}  k(t)\equiv(\frac{d\frac{1}{(S(t)^\expn{n-1)}}}{dt})\equiv(n-1)\omega[A_0]^{n-1} k(t)\equiv(\frac{d\frac{1}{(S(t)^{n-1)}}}{dt})\equiv(n-1)\omega[A_0]^{n-1}  \end{equation}  As shown in equation 4, the statistical length is the integral of the cumulative time dependent rate coefficient over a period of time $\Delta{t}$. The statistical length is   \begin{equation}  \mathcal{L}(\Delta t)^2=\left[\int_{t_i}^{t_f}\sqrt{(n-1)\omega([A]_0^\expn{n-1})}dt\right]^2 t)^2=\left[\int_{t_i}^{t_f}\sqrt{(n-1)\omega([A]_0^{n-1})}dt\right]^2  \end{equation}  Following length, the Fisher divergence is the integral of the cumulative time dependent rate coefficient squared over a period of time $\Delta{t}$. The Fisher divergence is  \begin{equation}  \frac{\mathcal{J}( \Delta t)}{\Delta t}=\int_{t_i}^{t_f}{(n-1)^2\omega^2}([A_0]^\expn{n-1})^\expn{2}}} t}=\int_{t_i}^{t_f}{(n-1)^2\omega^2}([A_0]^{n-1})^{2}}}  dt \end{equation}  The inequality becomes  \begin{equation}  (n-1)^2\omega^2([A_0]^\expn{n-1})^2\Delta t^2-[(n-1)\omega[A_0]^\expn{n-1}\Delta (n-1)^2\omega^2([A_0]^{n-1})^2\Delta t^2-[(n-1)\omega[A_0]^{n-1}\Delta  t]^2\geq0 \end{equation}  Again, we see that when the bound $(n-1)^2\omega^2([A_0]^\expn{n-1})^\expn{2}\Delta t^2=[(n-1)\omega[A_0]^\expn{n-1}\Delta $(n-1)^2\omega^2([A_0]^{n-1})^{2}\Delta t^2=[(n-1)\omega[A_0]^{n-1}\Delta  t]^2$ holds, there is no static or dynamic disorder, and a single rate coefficient can be defined for the irreversible decay process.