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\end{cases}  \end{equation}  \section{Bound \subsection{Bound  for constant rate coefficients} These forms of $k(t)$ satisfy the bound $\mathcal{J}-\mathcal{L}^2 = 0$ in the absence of disorder, when $k_i(t)\to\omega$. This is straightforward to show for the case of an $i^{th}$-order reaction, with the traditional integrated rate law  \begin{equation}