In this preprint a system of evolution equations for energy models of a semiconductor device is derived on an deductive way from a generally accepted expression for the free energy. Only first principles like the entropy maximum principle and the principle of partial local equilibrium are applied. Particular attention is paid to include the electrostatic potential self-consistently. Dynamically ionized trap levels and models with carrier temperatures are regarded. The system of evolution equations is compatible with the corresponding entropy balance equation that contains a positively definite entropy production rate
