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\section{Introduction}  Rates are a nearly universal characterization of naturally characterize  kinetic processes. There In chemistry, determining the macroscopic rates of chemical reactions is one approach to learn the microscopic mechanism. The mass-action rate laws  are many instances where empirical results, assuming  the reaction system is homogeneous with uniform concentration(s) throughout. Heterogeneity and fluctuations in structure, energetics, or concentrations can cause deviations from traditional rate laws. When  traditional kinetics model does is  not sufficiently describe a population decaying over time sufficient  [insert citation]. These cases are more accurately described by either citation], theoretical approaches adopt  a distribution of rate coefficients, or a time dependent rate coefficient, defined as static or dynamic disorder respectively coefficient. Statically and dynamically disordered kinetics  [insert citation]. Therefore the Zwanzig citation] are common...  The  ability to quantify these types of potentially inclusive disorders 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 highter oreder 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]. 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.