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