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In second order, Rate coefficients are a vital part of any kinetics experiment. There are many instances in classical kinetics where  the single rate coefficient model does not sufficiently describe a population decaying over  time dependent [insert citation]. The overall  rate coefficient may depend of a distribution of rate coefficients or may be time dependent, respectively known as static and dynamic disorder[insert citation]. Both static and dynamic disorder have mostly been studied in first order irreversible decay reactions[insert citation], but has now been studied in second, mixed second, and $n^{th}$ order irreversible decay. An inequality between two important quantities known as the statistical length and Fisher divergence  is able to quantitatively measure  the time derivative amount of static and dynamic disorder  of a rate coefficient over a period of time and is able to determine when traditional kinetics is truly valid[insert citation]. When the inequality is minimized,  the inverse statistical description  of rate coefficients is also minimized, which can help one determine  the survival function[insert citation]  \begin{equation}  \frac{dS(t)^{-1}}{dt}=k(t)   \end{equation}  Now consider best data set to use during  a population kinetic analysis. This inequality measures the temporal and spatial variation in the rate coefficient. When there is no static or dynamic disorder, this inequality is reduced to an equality and it is the only time where traditional kinetics is truly valid.   It has recently been shown that an inequality between the statistical length squared and the divergence can numerically represent how constant a rate coefficient is  of some species A a population irreversibly  decaying into B following over time in first order[insert citation]. This inequality is derived from  the reaction $A+A\rightarrow B$. The second first  orderintegrated  rate law is [cite]  \begin{equation}  [A_t]=\frac{[A_0]}{1+\omega t[A_0]}  \end{equation}  The second order and  survival function function. In traditional kinetics, irreversible decay  is \begin{equation}  S(t)=\frac{[A_t]}{[A_0]}=\frac{1}{1+\omega t[A_0]}  \end{equation}  The time only  dependent on one  rate coefficient for coefficient, $\omega$, and the mechanism of the reaction. The rate law of  a second first  order reaction of A irreversibly decaying into B  is \begin{equation}  k(t)=\left(\frac{dS(t)^{-1}}{dt}\right)=\frac{d}{dt}\left[1+\omega t[A_0]\right]=\omega[A_0] \frac{-dA}{dt}=\omega[A]  \end{equation}  S(t) has been changed to fit a second order model The mechanism  of each  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 decay reaction may  be applied to survival functions and rate coefficients.[cite] Integrating different. For example,  the arc length irreversible decay  of A into B may follow second order kinetics, where  the survival curve , $\frac{1}{S(t)}$, gives the statistical length. rate law is  \begin{equation} \mathcal{L}(\Delta{t})=\int_{t_i}^{t_f}k(t)dt \frac{-dA}{dt}=\omega[A]^2  \end{equation} Which is equal to $\frac{1}{S(t)}\big|_{S_(t_f)}^{S_(t_i)}$, which measures the cumulative The time dependent  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. To form an inequality, another quantity called the Fisher divergence is calculated, which k(t),  is defined as [cite]  \begin{equation}  \frac{\mathcal{J}(\Delta{t})}{\Delta{t}}=\int_{t_i}^{t_f}k(t)^{2}dt  \end{equation}  It has been shown that in first order kinetics determined by integrating  the inequality between rate law of  the statistical length squared reaction  and Fisher divergence determines when forming  a survival function from the integrated  rate coefficient is constant, which is only when law. From  the inequality turns into an equality.[cite] A similar inequality is found in second order kinetics. The inequality between statistical length squared and Fisher divergence is  \begin{equation}  \mathcal{L}(\Delta{t})^2\leq \mathcal{J}(\Delta{t})  \end{equation}  Which also means that  \begin{equation}  \mathcal{J}(\Delta{t})-\mathcal{L}(\Delta{t})^2\geq 0  \end{equation}  \begin{equation}  \Delta{t}\int_{t_i}^{t_f}k(t)^{2}dt-\left[{\int_{t_i}^{t_f}k(t)dt\right]^{2}dt\geq0  \end{equation}  Putting in survival function,  the time dependent rate coefficientfor a second order irreversible decay, the inequality becomes  \begin{equation}  \omega^2[A_0]^2\Delta{t}^2-\left(\omega[A_0]\Delta{t}\right)^2\geq0  \end{equation}  This result  is very similar to that determined by taking various time derivatives  offirst order irreversible decay($\omega^2\Delta{t}^2-\left(\omega\Delta{t}\right)^2\geq0$),  the only difference being a dependence survival function, depending  on the initial concentration total order  of the reactant. This initial concentration dependence serves to cancel the concentration units in the second reaction. For first  order rate coefficient, making irreversible decay reactions,  thestatistical length and Fisher divergence dimensionless. When there is a  time independent dependent  rate coefficientand there  isno static disorder,  the equality holds $\omega^2[A_0]^2\Delta{t}^2=\left(\omega[A_0]\Delta{t}\right)^2$. negative time derivative of the natural log of the survival function[insert citation]  \begin{equation}  \frac{-dlnS(t)}{dt}=k(t)   \end{equation}