Entropy production and choice of heat flux for degenerate semiconductors and metals

The concept of heat flux in multi‐band solids, having built‐in fields, is definable in various ways, depending on which energies are included in the transport. First the macroscopic entropy balance is examined, though more insight is gained from a microscopic picture. To this purpose the entropy flux and production function are computed for a degenerate nonuniform electron gas from the Boltzmann equation, using the streaming‐vector method, up to first order terms. From this a consistent picture of total energy, internal energy, and entropy transport emerges. The Boltzmann H‐theorem for electron—phonon interaction is also briefly discussed.