deletions | additions       diff --git a/Introduction.tex b/Introduction.tex  index 848e812..958b748 100644  --- a/Introduction.tex  +++ b/Introduction.tex 
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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 Reference~1  showed how 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 inequality result  todisorder in  irreversible decay processes with order ``order''  higher than one. We show $\mathcal{J}-\mathcal{L}^2$ $\mathcal{J}-\mathcal{L}^2=0$  is a condition for a  constant rate coefficients. coefficient for any $i$.  Accomplishing this end requires reformulating the definition of the time-dependent rate coefficient. An %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]. 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 valid. 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 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 kineticsand mixed order kinetics  for irreversible decay phenominium. phenomena.  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. We consider the irreversible elementary reaction types  \begin{equation}