不可逆衰变过程中的有序与无序
Order and disorder in irreversible decay processes
摘要：
动力学无序激发了唯象质量作用速率方程中的波动速率系数。在这些速率方程中，反应级数是控制速率对物种数依赖性的固定指数。在这里，我们澄清这些概念之间的关系（无序）为了在不可逆的衰变，$n\,A\to B$，$n=1,2,3,\ldots$，通过扩展的速率系数波动的理论措施。测量值$\mathcal{J}_n-\mathcal{L}_n^2\geq 0$是$\mathcal{J}_n$与$\mathcal{L}_n^2$之间不等式的大小，$\mathcal{J}_n$是速率系数乘以感兴趣的时间间隔的时间积分平方，$\mathcal{L}_n^2$是时间积分速率系数的平方。将不等式应用于非指数松弛的经验模型，我们证明了它量化了速率系数与常数的累积偏差，从而量化了动力学紊乱的程度。等式是传统动力学满足的界限，其中单个速率常数就足够了。对于这些模型，我们展示了如何增加反应顺序可以增加或减少动力学无序，以及如何，在任何一种情况下，不等式$\mathcal{J}_n-\mathcal{L}_n^2\geq 0$可以表示推断的能力，在动态无序动力学的反应顺序。
英文摘要：
Dynamical disorder motivates fluctuating rate coefficients in phenomenological, mass-action rate equations. The reaction order in these rate equations is the fixed exponent controlling the dependence of the rate on the number of species. Here we clarify the relationship between these notions of (dis)order in irreversible decay, $n\,A\to B$, $n=1,2,3,\ldots$, by extending a theoretical measure of fluctuations in the rate coefficient. The measure, $\mathcal{J}_n-\mathcal{L}_n^2\geq 0$, is the magnitude of the inequality between $\mathcal{J}_n$, the time-integrated square of the rate coefficient multiplied by the time interval of interest, and $\mathcal{L}_n^2$, the square of the time-integrated rate coefficient. Applying the inequality to empirical models for non-exponential relaxation, we demonstrate that it quantifies the cumulative deviation in a rate coefficient from a constant, and so the degree of dynamical disorder. The equality is a bound satisfied by traditional kinetics where a single rate constant is sufficient. For these models, we show how increasing the reaction order can increase or decrease dynamical disorder and how, in either case, the inequality $\mathcal{J}_n-\mathcal{L}_n^2\geq 0$ can indicate the ability to deduce the reaction order in dynamically disordered kinetics.
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