Jason R. Green edited Introduction.tex  over 9 years ago

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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 and mixed order kinetics for irreversible decay phenominium. 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.  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]. When the inequality is minimized, the statistical description of rate coefficients is also minimized, which can help one determine the best data set to use during a kinetic analysis. 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 truly valid. This inequality has been interpreted as a measure of how constant a rate coefficient can be. 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 gernealizing to higher order kinetics. We consider the irreversible elementary reaction types  \begin{eqnarray}  A &\to& \mathrm{products}\\  A^2 &\to& \mathrm{products}\\  \vdots\\  A^n &\to& \mathrm{products}\\  \end{eqnarray}