On thermopower calculations with temperature dependent electron energies

It is argued that the thermoeletric transport coefficients in a coupled electron-phonon system depend on the interaction of phonons with a heat bath. When the phonon mean free path is short, the temperature dependent energy levels may be introduced in the Boltzmann equation which yields the usual formulae for the thermopower with temperature dependent energies inserted. For weak phonon-heat bath interaction and strong electron-phonon interaction the transport equation is obtained for new quasiparticles and the energy current includes the transport of the electron-phonon energies carried along by a quasiparticle.