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Shane Flynn edited Pre-Theory Background.tex
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\subsection{Fisher Information}
The definition and meaning of the Fisher Information is a rather subtle but powerful mathematical concept. It should be thought of as a way to statistically measure a parameter. Based on our definition this information is again motivated as a type of variance, however it measures the fluctuations in the survival function itself. The Fisher information was proposed by Fisher as follows.
\begin{equation}
I(t)=\sum \gamma_i(\frac{d}{dt}[ln\sum
\gamma_i]) \gamma_i])^2
\end{equation}
\subsection{Inequality}
The main result of our previous work was an inequality, which becomes an equality only when there is no disorder acting on the system. This inequality therefore provides a method for quantifying the amount of disorder (static and/or dynamic not exclusive) present in the system. This inequality is a reconstruction of the Cauchy-Schwartz Inequality and is therefore a mathematical truth describing the system of interest. To construct the inequality any first order irreversible decay process can be analyzed, experimentally the survival function provides all the measurements necessary to construct the inequality, therefore only the time dependent concentration throughout the reaction is necessary to complete the analysis.