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\section{Nonlinear irreversible kinetics}  We consider the irreversible reaction types  \begin{equation}  A^i \to \mathrm{products}\quad\quad\textrm{for}\quad i=1,2,3,\ldots,n  \end{equation}  with the nonlinear differential rate laws  \begin{equation}  \frac{dC_i(t)}{dt} = k_i(t)\left[C_i(t)\right]^i.  \end{equation}  Experimental data corresponds to the integrated form of the rate law, a concentration profile. For example, in the case of the $i^{th}$-order reaction, the traditional integrated rate law and a rate ``constant'', $k_i(t)\to\omega$, is  \begin{equation}  \frac{1}{C_i(t)^{i-1}} = \frac{1}{C_i(0)^{i-1}}+(i-1)\omega t.  \end{equation}  Normalizing the concentration profile, by comparing the concentration at a time $t$ to the initial concentration, leads to the survival function  \begin{equation}  S_i(t) = \frac{C_i(t)}{C_i(0)} = \sqrt[i-1]{\frac{1}{1+(i-1)\omega tC_i(0)^{i-1}}},  \end{equation}  which we will use as the input to our theory.  From the survival function, we define the time-dependent rate coefficient through an appropriate time derivative depending on the total order of reaction. For first-order irreversible decay reactions, $A\to \textrm{products}$ and $i=1$, the rate law defines the time-dependent rate coefficient  \begin{equation}  k_1(t) \equiv \frac{-d\ln S_1(t)}{dt}  \end{equation}  In traditional kinetics, the rate coefficient irreversible decay is assumed constant, in which case $k(t)\to\omega$. 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}