Joule heating in Boltzmann theory of metals

Boltzmann theory deals with the quasiparticle distributions FK for electrons and NQ for phonons. It is difficult to reconcile the common situation of "steady state"(where distributions are out of equilibrium but carry steady charge current j-) and Joule heating j-·E-. This paper offers elementary clarification. The resolution is simplest if a true steady state is abandoned.