= Entropy loss of an isolated convective planet
{title2=$L_{\rm int}=-\int T\dot s\,dm$}
With negligible nuclear or external heating, the <stellar structure equations> give $L_{\rm int}=-\int_0^M T\,\partial s/\partial t\,dm$. A nearly isentropic convective interior therefore has $\dot s=-L_{\rm int}/\int T\,dm<0$ whenever it radiates. Decreasing <specific entropy> does not require temperature at every depth to decrease immediately: contraction of an <ideal gas> can raise its central temperature while total energy is lost.
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