Thermal Landau quasiparticle energy shift
= Thermal Landau quasiparticle energy shift
For a symmetric interaction kernel, $\delta E/\delta n_a=\epsilon_a+V^{-1}\sum_bf_{ab}\delta n_b$. Smooth Fermi-surface kernels and fixed-density chemical-potential shifts give an $O(T^2)$ thermal correction by the <Sommerfeld expansion>. The reference dispersion already includes zero-temperature interactions.