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\section{Definition of time-dependent rate coefficient}  From the survival function, we define  the time dependent time-dependent  rate coefficient is determined by taking various through an appropriate  time derivatives derivative  of the survival function, depending which depends  on the total order of reaction. For first order first-order  irreversible decay reactions, $A\to B$, the rate law defines the time dependent 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 %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. In order to determine We define  $k(t)$ in higher order reactions, we use from  the appropriate  survival function, but it is not necessary. From the survival function, the time dependent function and  rate coefficient is law  \begin{equation}  k_i(t) \equiv \frac{d}{dt}\frac{1}{S(t)^{i-1}} \frac{d}{dt}\frac{1}{S(t)^{i-1}}.  \end{equation}