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Jason R. Green edited $n^{th}$-order decay.tex
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\section{$n^{th}$-order decay, $A^n\to P$}
We now shift our attention to $n^{th}$ order reactions. These $n^{th}$ order reactions are of the form of one reactant turning into product. The inequality between the statistical
distance length and
Fisher divergence can also be derived for these irreversible decay reactions. The time dependent rate coefficient is
\begin{equation}
k_n(t)
\equiv
(\frac{d\frac{1}{(S(t)^{n-1)}}}{dt})\equiv(n-1)\omega[A_0]^{n-1} \frac{d}{dt}\frac{1}{S(t)^{n-1}}
= (n-1)\omega C_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}