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\begin{equation}  \frac{\mathcal{J}(\Delta{t})}{\Delta{t}} = \int_{t_i}^{t_f}k(t)^{2}dt  \end{equation}  over a time interval $\Delta t = t_f - t_i$. Both $\mathcal{L}$ and $\mathcal{J}$ 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 processes  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. For this work we propose An inequality between two important quantities known as the statistical length and Fisher divergence is able to quantitatively measure the amount of static and dynamic disorder of a rate coefficient over  a generalization period  of our previous first order irreversible decay time, and is able to determine when traditional  kinetics is truly valid[insert citation]. This inequality measures the temporal and spatial variation in the rate coefficient. When there is no static or dynamic disorder, this inequality is reduced  to higher orders, an equality and it is the only time where traditional kinetics is valid. It captures the fluctuations associated  with complete framework analyzing any $n^{th}$ the rate coefficient for first  order system with this description. irreversible decay processes.  In this work we expand on this idea providing more generality and utility to the theory by generalizing to higher-order kinetics. For this work we propose a generalization of our previous first order irreversible decay kinetics to higher orders, with complete framework analyzing any $n^{th}$ order system with this description. In this work we  propose a method for studying these more complex cases in chemical kinetics proposing theory to analyze disorder in $n^{th}$ order kinetics and provide detailed proof-of-principle analyses for second order kinetics and mixed order kinetics for irreversible decay phenominium. We then connect this theory to previously accepted work on first order kinetics showing how the model simplifies in a consistent manner when working with first order models.An inequality between two important quantities known as the statistical length and Fisher divergence is able to quantitatively measure the amount of static and dynamic disorder of a rate coefficient over a period of time, and is able to determine when traditional kinetics is truly valid[insert citation]. When the inequality is minimized, the statistical description of rate coefficients is also minimized, which can help one determine the best data set to use during a kinetic analysis. This inequality measures the temporal and spatial variation in the rate coefficient. When there is no static or dynamic disorder, this inequality is reduced to an equality and it is the only time where traditional kinetics is truly valid. This inequality has been interpreted as a measure of how constant a rate coefficient can be. It captures the fluctuations associated with the rate coefficient for first order irreversible decay processes. In this work we expand on this idea providing more generality and utility to the theory by gernealizing to higher order kinetics.  We consider the irreversible elementary reaction types  \begin{equation}  A^i \to \mathrm{products}\quad\quad\textrm{for}\quad i=1,2,3,\ldots,n  \end{equation}  with the mass-action rate laws  \begin{equation}  \frac{dC_{A^i}(t)}{dt} = k_iC_{A^i}(t).  \end{equation}  Experimentalists deduce rate laws from data that is the integrated rate law. For the $i^{th}$-order reaction the integrated rate law is  \begin{equation}  \frac{1}{[C_A(t)]^{i-1}} = \frac{1}{[C_A(0)]^{i-1}}+(i-1)\omega t.  \end{equation}  Survival functions are the input to our theory  \begin{equation}  S(t) = \frac{C_A(t)}{C_A(0)},  \end{equation}  which come from the integrated rate law. The survival function for this class of reactions is  \begin{equation}  S(t) = \sqrt[i-1]{\frac{1}{1+(i-1)\omega tC_A(0)^{i-1}}}  \end{equation}