deletions | additions       diff --git a/Second-order decay.tex b/Second-order decay.tex  index 80c110d..f021580 100644  --- a/Second-order decay.tex  +++ b/Second-order decay.tex 
...
\section{Second-order decay, $A+A\to P$}  In second order, we define  the time dependent rate coefficient is as  the time derivative of the inverse of the survival function[insert citation]\begin{equation}  \frac{dS(t)^{-1}}{dt}=k(t)   \end{equation}    Which is equal to  \begin{equation}  k(t)=\left(\frac{dS(t)^{-1}}{dt}\right)=\frac{d}{dt}\left[1+\omega t[A_0]\right]=\omega[A_0] k(t) \equiv \frac{d}{dt}S(t)^{-1} = \omega C_A(0)  \end{equation}  S(t) $S(t)$  has been changed to fit a second order model of irreversible decay. From this definition of k(t), $k(t)$,  we define a statistical distance . distance.  The statistical distance represents the distance between two different probability distributions, which can be applied to survival functions and rate coefficients.[cite] Integrating the arc length of the survival curve , $\frac{1}{S(t)}$, gives the statistical length. \begin{equation}  \mathcal{L}(\Delta{t})^2=\left[\int_{t_i}^{t_f}k(t)dt\right]^2  \end{equation}