Reservoir relaxation test for a chemical steady state (${\tau }_{\mathrm{relax}}=1/k$)

For $dX/dt=P-kX$ with locally fixed coefficients, $X(t)=P/k+(X_0-P/k)e^{-kt}$. Setting $dX/dt\simeq 0$ requires $1/k$ to be short compared with changes in production, loss and transport. A major reservoir can fail this test even when nearby radicals rapidly adjust.