  Dynamical disorder motivates fluctuating rate coefficients in
phenomenological, mass-action rate equations. The reaction order in these rate
equations is the fixed exponent controlling the dependence of the rate on the
number of species. Here we clarify the relationship between these notions of
(dis)order in irreversible decay, $n\,A\to B$, $n=1,2,3,\ldots$, by extending a
theoretical measure of fluctuations in the rate coefficient. The measure,
$\mathcal{J}_n-\mathcal{L}_n^2\geq 0$, is the magnitude of the inequality
between $\mathcal{J}_n$, the time-integrated square of the rate coefficient
multiplied by the time interval of interest, and $\mathcal{L}_n^2$, the square
of the time-integrated rate coefficient. Applying the inequality to empirical
models for non-exponential relaxation, we demonstrate that it quantifies the
cumulative deviation in a rate coefficient from a constant, and so the degree
of dynamical disorder. The equality is a bound satisfied by traditional
kinetics where a single rate constant is sufficient. For these models, we show
how increasing the reaction order can increase or decrease dynamical disorder
and how, in either case, the inequality $\mathcal{J}_n-\mathcal{L}_n^2\geq 0$
can indicate the ability to deduce the reaction order in dynamically disordered
kinetics.
