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Fluctuating rate coefficients are necessary when modeling disordered kinetic processes with mass-action rate equations. However, measuring the fluctuations of rate coefficients is a challenge, particularly for nonlinear rate equations. Here we present a measure of the total disorder in irreversible decay $i\,A\to \textrm{products}$, $i=1,2,3,\ldots n$ governed by (non)linear rate equations -- 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. We apply the theory to empirical models for statically and dynamically disordered kinetics with $i\geq 2$. These models serve to demonstrate that the inequality is the cumulative deviation in a  rate coefficients coefficient  from a constant value, constant,  and the equality is a bound only satisfiedby the rate equations  when the rate coefficients are constant in time.