deletions | additions       diff --git a/Second-order decay.tex b/Second-order decay.tex  index f021580..fc9c077 100644  --- a/Second-order decay.tex  +++ b/Second-order decay.tex 
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In second order, we define the time dependent rate coefficient as the time derivative of the inverse of the survival function[insert citation]  \begin{equation}  k(t) k_2(t)  \equiv \frac{d}{dt}S(t)^{-1} = \omega C_A(0) \end{equation}  $S(t)$ has been changed to fit a second order model of irreversible decay. From this definition of $k(t)$, we define a statistical 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}  Which is equal to $\frac{1}{S(t)}\big|_{S_(t_f)}^{S_(t_i)}$, which measures the cumulative rate coefficient, same as in first order irreversible decay. As seen in first order, the statistical length is also dependent on the time interval, with the statistical length being infinite in an infinite time interval.   In first order irreversible decay, the inequality between the statistical length squared and Fisher divergence determines when a rate coefficient is constant, which is only when the inequality turns into an equality.[cite] A similar inequality is found in second order kinetics.