Temperature-dependent energy levels and the second law formulation for engineering devices

We shall give an overview, within a scope of the author's knowledge, on
fundamental importance of the temperature dependency of energy levels in materials
in quantifying heat dissipated in thermodynamically operated devices. After a brief review of the
relevant studies of temperature dependency in semiconductors, we point out that entropy produced
or heat dissipated in thermoelectric devices based on thermoelectric effects such as Peltier, Seebeck
and Thomson can be reformulated by inclusion of the effect of temperature-dependent energy levels in
materials (semicondactors). Statistical mechanics consideration for the origin of the temperature
dependent energy levels is also given based on a general ensemble theory.