Peculiarities of Calculating Entropy in Self-Consistent Field Models

The calculation of entropy in the self-consistent field models faces some difficulties related to the entropy behavior peculiarities at low temperatures in the models with different degrees of specification of the electron energy spectrum. This paper considers the behavior of the electron entropy in two self-consistent field models that have been widely used lately, namely the Liberman model and the quasi-zone model. Special attention is focused on low temperatures. In particular, it is shown that the entropy of electrons in the Liberman model at low densities and the temperature $T = 0$ takes on nonzero values which differ in the relativistic and nonrelativistic versions of the model. The electron entropy in the quasi-zone model at low densities of the matter and $T = 0$ is zero. In addition, it is shown that at low temperatures and high densities the entropy in the Liberman model smoothly turns to the asymptotic form of the Thomas–Fermi (TF) model, while such a smooth transition to the TF asymptotic form is not always observed in the quasi-zone model.