Thermal Landau quasiparticle energy shift

For a symmetric interaction kernel, $\delta E/\delta n_a={ϵ}_a+V^{-1}{\sum }_b{f}_{ab}\delta n_b$. 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.