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Fluctuating rate coefficients are necessary to describe disordered kinetic processes with phenomenological, mass-action rate laws. Linear rate laws for irreversible decay have been the primary focus of this approach, but kinetic processes with nonlinear rate laws may also show disorder. Here we present a measure of the total disorder, static or dynamic, in irreversible decay for $A^n\to \textrm{products}$, $n=1,2,3,\ldots$. The We  measureof the rate coefficient history we introduce is  the inequality between the time-integrated square of the rate coefficient (multiplied by the time interval of interest) and the square of the time-integrated rate coefficient. Applying this measure of the rate coefficient history  to empirical models for disordered kinetics of order $n\geq 2$ shows this inequality measures the cumulative deviations in rate coefficients from a constant value for this class of kinetic processes. The equality is a necessary and sufficient condition for the traditional kinetics rate laws  with ``rate constants'' to hold.