= First-order thermal isolation
{title2=$C\dot{\delta T_s}+G\delta T_s=G\delta T_b+\delta P$}
A lumped sample of <heat capacity> $C$ coupled by <thermal conductance> $G$ to a bath has the displayed linearized <energy> balance. For constant internal power, the bath-to-sample <temperature> response is $1/(1+i\omega C/G)$. Insulation and <heat capacity> suppress rapid bath fluctuations but have unity static bath-to-sample gain. A steady power change shifts the sample by $\delta P/G$, so improved isolation increases self-heating sensitivity and equilibration time. The lumped approximation requires internal equilibration faster than the variations being modeled.
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