Influence of electron and phonon temperature on the efficiency of thermoelectric conversion

In the framework of Extended Irreversible Thermodynamics it is developed a two-temperature model (for electrons and phonons, respectively) of thermoelectric effects. The expression of the maximum efficiency in terms of these two temperatures is derived as well. It is proved that, for the electron temperature higher than the phonon temperature, the two-temperature model yields an efficiency which is higher with respect to that of the single-temperature model. Two possible experiments to estimate the electron temperature are suggested.