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The ability to quantify disorder is essential information for understanding your system. In our previous work a theory was developed for analyzing first order irreversible decay kinetics through an inequality[insert citation]. The convenience of this inequality is through its ability to quantify disorder, with the unique property of becoming an equality only when the system is disorder free, and therefore described by chemical kinetics in its classical formulation. The next problem that should be addressed is that of higher order kinetics, what if the physical systems one wishes to understand are more complex kinetic schemes, they would require a modified theoretical framework for analysis, but should and can be addressed. To motivate this type of development systems such as...... are all known to proceed through higher ordered kinetics, and all of these systems possess unique and interesting applications, therefore a more complete kinetics description of them should be pursued[insert citations].   The main result in Reference[cite] is an inequality  \begin{equation}  \mathcal{L}(\Delta{t})^2\leq \mathcal{J}(\Delta{t})  \end{equation}  between the statistical length (squared)  \begin{equation}  \mathcal{L}(\Delta{t})^2 = \left[\int_{t_i}^{t_f}k(t)dt\right]^2  \end{equation}  and the divergence  \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 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 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.