deletions | additions       diff --git a/Absolute Formulation.tex b/Absolute Formulation.tex  index 9a56331..907cd3e 100644  --- a/Absolute Formulation.tex  +++ b/Absolute Formulation.tex 
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\begin{equation}  GFE_a=\sum[\gamma_i\frac{d}{dt}[k_a]]-(\sum k_a\gamma_i)^2+\sum[k_a^2\gamma_i]=\sum[\gamma_i\frac{d}{dt}[k_a]]-(\overline{k})^2+\overline{k_a^2}  \end{equation}  We can now take the $GFE_a$ and analyze the simplest model, two different states A and A' with associated survival functions $e^{-\omega t}$ and $e^{-\omega't}$.  \begin{equation}  \frac{e^{-\omega t}}{e^{-\omega t}+e^{-\omega't}}\frac{d}{dt}[e^{-\omega t}]+\frac{e^{-\omega't}}{e^{-\omega t}+e^{-\omega' t}}\frac{d}{dt}[e^{-\omega't}]-(\frac{e^{-\omega t}}{e^{-\omega t}+e^{-\omega't}}\frac{d}{dt}[e^{-\omega t}]+\frac{e^{-\omega't}}{e^{-\omega t}+e^{-\omega' t}}\frac{d}{dt}[e^{-\omega't}])^2+\frac{e^{-\omega t}}{e^{-\omega t}+e^{-\omega't}}(\frac{d}{dt}[e^{-\omega t}])^2+\frac{e^{-\omega't}}{e^{-\omega t}+e^{-\omega' t}}(\frac{d}{dt}[e^{-\omega't}])^2  \end{equation}  If we now take the limiting case of no disorder and only 1 A state where $\omega=\omega'\equiv u$ we can see the most simplified application of this formulation.   \begin{equation}  GFE_a=-ue^{-ut}  \end{equation}  \subsection{Inequality}