deletions | additions       diff --git a/Introduction.tex b/Introduction.tex  index 433431e..5c70539 100644  --- a/Introduction.tex  +++ b/Introduction.tex 
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%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 kinetics for irreversible decay 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 reaction types  \begin{equation}  A^i \to \mathrm{products}\quad\quad\textrm{for}\quad i=1,2,3,\ldots,n  \end{equation}  with the differential rate laws  \begin{equation}  \frac{dC_i(t)}{dt} = k_i(t)\left[C_i(t)\right]^i.  \end{equation}  Experimental data corresponds to the integrated form of the rate law, a concentration profile. For example, in the case of the $i^{th}$-order reaction, the traditional integrated rate law and a rate ``constant'', $k_i(t)\to\omega$, is  \begin{equation}  \frac{1}{C_i(t)^{i-1}} = \frac{1}{C_i(0)^{i-1}}+(i-1)\omega t.  \end{equation}  Normalizing the concentration profile, by comparing the concentration at a time $t$ to the initial concentration, leads to the survival function  \begin{equation}  S_i(t) = \frac{C_i(t)}{C_i(0)} = \sqrt[i-1]{\frac{1}{1+(i-1)\omega tC_i(0)^{i-1}}},  \end{equation}  which we will use as the input to our theory.