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The most important piece in extending current theory to higher order irreversible decay is determining the time dependent rate coefficient. The statistical length and divergence are both functions of the time dependent rate coefficient.  \begin{equation}  \mathcal{L}(\Delta{t})=\int_{t_i}^{t_f}k(t)dt \mathcal{L}(\Delta{t})^2=\left[\int_{t_i}^{t_f}k(t)dt\right]^2  \end{equation}  \begin{equation}  \frac{\mathcal{J}(\Delta{t})}{\Delta{t}}=\int_{t_i}^{t_f}k(t)^{2}dt