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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 [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 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 statistical description of rate coefficients is also minimized, which can help one determine the best data set to use during a 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 In second order,  thedivergence can numerically represent how constant a rate coefficient is of a population irreversibly decaying over  timein first order[insert citation]. This inequality is derived from the first order rate law and survival function. In traditional kinetics, irreversible decay is only  dependenton one  rate coefficient, $\omega$, and the mechanism of the reaction. The rate law of a first order reaction of A irreversibly decaying into B coefficient  is \begin{equation}  \frac{-dA}{dt}=\omega[A]  \end{equation}  The mechanism the time derivative  ofeach irreversible decay reaction may be different. For example,  the irreversible decay inverse  ofA into B may follow second order kinetics, where  the rate law is survival function[insert citation]  \begin{equation}  \frac{-dA}{dt}=\omega[A]^2 \frac{dS(t)^{-1}}{dt}=k(t)  \end{equation}  Now consider a population of some species A decaying into B following the reaction $A+A\rightarrow B$. The second order integrated rate law is [cite]  \begin{equation}  [A_t]=\frac{[A_0]}{1+\omega t[A_0]}  \end{equation}  The second order survival function is  \begin{equation}  S(t)=\frac{[A_t]}{[A_0]}=\frac{1}{1+\omega t[A_0]}  \end{equation}  The time dependent rate coefficient, k(t), coefficient for a second order reaction  is determined by integrating \begin{equation}  k(t)=\left(\frac{dS(t)^{-1}}{dt}\right)=\frac{d}{dt}\left[1+\omega t[A_0]\right]=\omega[A_0]  \end{equation}  S(t) has been changed to fit a second order model of 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 be applied to survival functions and  rate law coefficients.[cite] Integrating the arc length  of thereaction and forming a  survival function from curve , $\frac{1}{S(t)}$, gives  the integrated statistical length.  \begin{equation}  \mathcal{L}(\Delta{t})=\int_{t_i}^{t_f}k(t)dt  \end{equation}  Which is equal to $\frac{1}{S(t)}\big|_{S_(t_f)}^{S_(t_i)}$, which measures the cumulative  rate law. From coefficient, same as in first order irreversible decay. As seen in first order,  the survival function, statistical length is also dependent on  the time dependent 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 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 the inequality between the statistical length squared and Fisher divergence determines when a  rate coefficient is determined by taking various time derivatives of constant, which is only when  the survival function, depending on 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  the total time dependent rate coefficient for 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  ofreaction. For  first order irreversible decay reactions, decay($\omega^2\Delta{t}^2-\left(\omega\Delta{t}\right)^2\geq0$), the only difference being a dependence on the initial concentration of the reactant. This initial concentration dependence serves to cancel the concentration units in the second order rate coefficient, making  the statistical length and Fisher divergence dimensionless. When there is a  time dependent independent  rate coefficient and there  is no static disorder,  the negative time derivative of the natural log of the survival function[insert citation]  \begin{equation}  \frac{-dlnS(t)}{dt}=k(t)   \end{equation} equality holds $\omega^2[A_0]^2\Delta{t}^2=\left(\omega[A_0]\Delta{t}\right)^2$.