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To describe disordered kinetic processes with phenomenological, mass-action rate laws it is necessary to introduce fluctuating rate coefficients. First-order rate laws for irreversible decay have been the primary focus of this approach, but higher-order kinetics may also be disordered. Here we present theory for disordered irreversible decay for $A^n\to \textrm{products}$, $n=1,2,3,\ldots$. The central result is an a measure of the cumulative deviations of the rate coefficient history from a constant value -- the  inequality between the square of the time-integrated rate coefficient and the time-integrated rate coefficient squared. Application of this theory to empirical models for disordered kinetics shows this inequality measures the variation in rate coefficients for this class of kinetic processes. Traditional kinetics is valid only when the equality holds.