= Chapman family lifetime versus relaxation time
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Under fast <Chapman cycle> partitioning, an <odd oxygen> family abundance $X$ can satisfy $\dot X=P-kX^2$. At equilibrium $P=kX_e^2$, its turnover lifetime is $X_e/P=1/(kX_e)$, while linearizing gives $\delta\dot X=-2kX_e\delta X$ and relaxation time $1/(2kX_e)$. A chemical lifetime is therefore not automatically an eigenmode relaxation time. The often-used expression $1/(2k_3[\mathrm O])$ also assumes ozone dominates the family abundance.
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