= Photon-scattering recoil heating
{title2=$\langle\Delta E\rangle=\mathbf P\cdot\mathbf p/M+(p^2+p'^2)/(2M)$}
Absorption of <momentum> $\mathbf p$ followed by emission of $\mathbf p'$ changes a free atom's <momentum> by $\mathbf p-\mathbf p'$. For isotropic emission of fixed magnitude, its mean <vector> is zero. The <energy> change then separates into a directional <work> term and two positive <recoil> terms. If absorption directions are also isotropic and uncorrelated with the initial <momentum>, the <work> term averages away. Equal incoming and outgoing <photon> magnitudes give two <recoil> energies per cycle.
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