Jason R. Green edited Introduction.tex  over 9 years ago

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%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]. 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 valid. It captures the fluctuations associated with the rate coefficient for first order irreversible decay processes.  In this work we expand on this idea providing more generality and utility to extend  the theory by generalizing to higher-order kinetics. For this work we propose a generalization application  of our previous first order this inequality to measure disorder in  irreversible decay kineticsto higher orders,  with complete framework analyzing any $n^{th}$ order system nonlinear rate laws (i.e., kinetics  with total ``order'' greater thane unity). We illustrate  this description. In this work we propose a method for studying these more complex cases in chemical kinetics proposing theory to analyze disorder in $n^{th}$ order kinetics and provide detailed framework with  proof-of-principle analyses for second order second-order  kinetics for irreversible decay phenomena. We then also  connect this theory to previously accepted previous  work on first order first-order  kinetics showing how the model simplifies in a consistent manner when working with first order models.