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\displaystyle +\frac{d}{dt}\frac{1}{S_i(t)^{i-1}} & \text{if } i \geq 2.  \end{cases}  \end{equation}  In traditional kinetics, the rate coefficient of irreversible decay is assumed constant, in which case $k(t)\to\omega$. However, this will not be the case when the kinetics are statically or dynamically disordered. In these cases, we will use the above definitions of $k(t)$.