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Jonathan Nichols edited Kinetic Model With Static Disorder.tex
over 9 years ago
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The difference between the Fisher Divergence and statistical length can also serve as a way of measuring the amount of static disorder in a second order irreversible decay processes. The same model used to show that this is true in first order irreversible decay can be examined again in second order. This model examines two experimentally indistinguishable states A and A', which inter-convert between each other[cite Plonka]. These two states eventually decay irreversibly into B with two time independent rate coefficients $\omega$ and $\omega$' describing the rates of
reaction. decay. It can be shown that when a distribution of rate coefficients is necessary ($\omega\neq\omega'$), the decay is bi-exponential in second order. When the rate coefficients $\omega$ and $\omega '$ are equal, the decay follows the second order survival function shown in equation 2. In a general case of any order, the survival function is
\begin{equation}
S(t) = \frac{N_A (t)+N_A' (t)}{N_A (0)+N_A' (0)}
\end{equation}