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\section{Definition of time-dependent rate coefficient}  From the survival function, we define the time-dependent rate coefficient through an appropriate time derivative of the survival function, which depends on the total order of reaction. For first-order irreversible decay reactions, $A\to B$, the rate law defines the time-dependent rate coefficient  \begin{equation}  k_1(t) \equiv \frac{-d\ln S(t)}{dt}  \end{equation}  In traditional kinetics, irreversible decay is only dependent on one rate coefficient, $k(t)\to\omega$.  %The time-dependent rate coefficient, $k(t)$, is determined by integrating the rate law of the reaction and forming a survival function from the integrated rate law.  We define $k(t)$ from the appropriate survival function and rate law  \begin{equation}  k_i(t) \equiv \frac{d}{dt}\frac{1}{S(t)^{i-1}}\quad\quad\textrm{for}\quad i=2,3,\ldots.  \end{equation}