deletions | additions       diff --git a/Introduction.tex b/Introduction.tex  index 5c70539..0b256b1 100644  --- a/Introduction.tex  +++ b/Introduction.tex 
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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].   Static and dynamic disorder lead to an observed rate coefficient that depends on time $k(t)$. The main result here, and  in Reference[cite] Reference[cite],  is an inequality \begin{equation}  \mathcal{L}(\Delta{t})^2\leq \mathcal{L}(\Delta{t})^2 \leq  \mathcal{J}(\Delta{t}) \end{equation}  between the statistical length (squared)  \begin{equation}  \mathcal{L}(\Delta{t})^2 = \equiv  \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}} = \equiv  \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]. Reference~1 showed that 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 result to irreversible decay processes with ``order'' higher than one. We show $\mathcal{J}-\mathcal{L}^2=0$ is a condition for a constant rate coefficient for any $i$. Accomplishing this end requires reformulating the definition of the time-dependent rate coefficient.