= Pomeranchuk cooling
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Low-<temperature> <solid> <helium-3> can have greater <entropy> than the <liquid> through disordered nuclear <spins>, enabling compression cooling. <The Pomeranchuk Effect by Robert Coleman Richardson>[Richardson, 1996 lecture, p.91, introduction and Fig.1]{ref}
The sign follows from the <Clapeyron equation>. Let $S_l,S_s$ be molar <entropies> and $V_l,V_s$ <molar volumes> of <liquid> and <solid>, respectively, on their <phase coexistence curve>. Equality of their <chemical potentials>, with $d\mu=-S\,dT+V\,dP$, gives
$$
\frac{dP}{dT}=\frac{S_l-S_s}{V_l-V_s}.
$$
With $S_s>S_l$ and $V_l>V_s$, the slope is negative. Reversibly <freezing> one mole at fixed <temperature> requires <heat> into the sample,
$$
Q_{l\to s}=T(S_s-S_l)>0,
\qquad L_{s\to l}=T(S_l-S_s)<0.
$$
Here $L_{s\to l}$ uses the melting convention for <latent heat of fusion>. This is the opposite sign from ordinary <ice> melting. The inequalities specify the regime; <freezing> does not universally cool a substance. In an approximately isolated sample, the growing higher-<entropy> phase draws on the sample's thermal <energy> instead of an external heater. Irreversible losses and incoming <heat> oppose the cooling.
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