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\section{Theory}  Central to the kinetic theory The main result  in Reference[cite] are two functions of a possibly time-dependent rate coefficient: the statistical length (squared) is an inequality  \begin{equation}  \mathcal{L}(\Delta{t})^2 = \left[\int_{t_i}^{t_f}k(t)dt\right]^2 \mathcal{L}(\Delta{t})^2\leq \mathcal{J}(\Delta{t})  \end{equation}  and between  the Fisher divergence statistical length (squared)  \begin{equation}  \frac{\mathcal{J}(\Delta{t})}{\Delta{t}} \mathcal{L}(\Delta{t})^2  = \int_{t_i}^{t_f}k(t)^{2}dt. \left[\int_{t_i}^{t_f}k(t)dt\right]^2  \end{equation}  They generally satisfy an inequality and the divergence  \begin{equation}  \mathcal{L}(\Delta{t})^2\leq \mathcal{J}(\Delta{t}). \frac{\mathcal{J}(\Delta{t})}{\Delta{t}} = \int_{t_i}^{t_f}k(t)^{2}dt  \end{equation}  To define the length and divergence, over a time interval $\Delta t = t_f - t_i$.  Both $\mathcal{L}$  and arrive at this inequality, we $\mathcal{J}$ are functions of a possibly time-dependent rate coefficient, originally motivated by an  adapted form of  the Fisher information[cite]. We showed how the difference $\mathcal{J}(\Delta t)-\mathcal{L}(\Delta t)^2$ is a measure of the variation in the rate coefficient, due to static or dynamic disorder, for decay kinetics with a first-order rate law. The lower bound holds only when the rate coefficient is constant in first-order irreversible decay. Here we extend this inequality to disorder in irreversible decay proecesses with order higher than one. We show $\mathcal{J}-\mathcal{L}^2$ is a condition for constant rate coefficients. Accomplishing this end requires reformulating the definition of the time-dependent rate coefficient. The survival function is a measure of the concentration of species at a time $t$ compared to the initial concentration  \begin{equation}