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\section{Introduction}  Rates are a way to infer the mechanism of kinetic processes, such as chemical reactions. They are often assumed to typically  obey the empirical mass-action rate laws, for example, laws  when the reaction system is homogeneous with uniform concentration(s) throughout. Deviations from traditional rate laws are possible when the system is heterogeneous and there are fluctuations in structure, energetics, or concentrations. When traditional kinetic descriptions break down [insert citation], the process is statically and/or dynamically disordered [insert Zwanzig citation], and it is necessary to replace the rate constant in the rate equation with a time-dependent rate coefficient or distribution of rate coefficients. coefficient.  Measuring the variation of time-dependent rate coefficients is a means of quantifying the fidelity of a rate coefficient and rate law. In our previous work a theory was developed for analyzing first order irreversible decay kinetics through an inequality[insert citation]. The magnitude usefulness  of the this  inequalityquantifies disorder -- the bound  is an equality satisfied in through its ability to quantify disorder, with  the absence unique property  of disorder, becoming an equality only  when traditional the system is disorder free, and therefore described by chemical  kinetics holds. Here we extend this theory to higher-order 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]. Static and dynamic disorder lead to an observed rate coefficient that depends on time $k(t)$. The main result here, and in Reference[cite], is an inequality  \begin{equation}