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Jonathan Nichols deleted file Abstract.tex
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Rate coefficients are a vital part of any kinetics experiment. There are many instances in classical kinetics where the single rate coefficient model does not sufficiently describe a population decaying over time [insert citation]. The overall rate coefficient may depend of a distribution of rate coefficients or may be time dependent, respectively known as static and dynamic disorder[insert citation]. Both static and dynamic disorder have mostly been studied in first order irreversible decay reactions[insert citation], but has now been studied in second, mixed second, and $n^{th}$ order irreversible decay. 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.
It has recently been shown that an inequality between the statistical length squared and the divergence can numerically represent how constant a rate coefficient is of a population irreversibly decaying over time in first order[insert citation]. This inequality is derived from the first order rate law and survival function. In traditional kinetics, irreversible decay is only dependent on one rate coefficient, $\omega$, and the mechanism of the reaction. The rate law of a first order reaction of A irreversibly decaying into B is
\begin{equation}
\frac{-dA}{dt}=\omega[A]
\end{equation}
The mechanism of each irreversible decay reaction may be different. For example, the irreversible decay of A into B may follow second order kinetics, where the rate law is
\begin{equation}
\frac{-dA}{dt}=\omega[A]^2
\end{equation}
The time dependent rate coefficient, k(t), is determined by integrating the rate law of the reaction and forming a survival function from the integrated rate law. From the survival function, the time dependent rate coefficient is determined by taking various time derivatives of the survival function, depending on the total order of reaction. For first order irreversible decay reactions, the time dependent rate coefficient is the negative time derivative of the natural log of the survival function[insert citation]
\begin{equation}
\frac{-dlnS(t)}{dt}=k(t)
\end{equation}
