= Adiabatic elimination
<Adiabatic elimination> replaces a rapidly relaxing variable by its instantaneous stable quasistatic value. If $\dot R=-\Gamma(t)R+P(t)$ with $\Gamma>0$, write $R=R_0+\delta R$, $R_0=P/\Gamma$. Then $\dot{\delta R}+\Gamma\delta R=-\dot R_0$. After the transient, $\delta R\simeq-\dot R_0/\Gamma$ when coefficients vary slowly compared with $\Gamma^{-1}$. This gives both the leading reduction and its time-scale error; rapid relaxation alone does not justify an additional Taylor expansion in another parameter.
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