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To describe disordered kinetic processes with phenomenological rate laws it is necessary to introduce fluctuating rate coefficients. The primary focus of this approach has been on first-order rate laws for irreversible decay, though higher-order kinetics may also be disordered. Here we present theory for disordered irreversible decay that is higher than first order, for  $A^n\to \textrm{products}$, $n=2,3,\ldots$. $n=1,2,3,\ldots$.  The central result is an inequality for time-integrated rate coefficient (squared) 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.