Thermodynamics in Density-Functional Theory and Force Theorems

The density-functional (DF) theory provides a simple method for calculating the properties of an interacting system under an external potential by associating it with a corresponding non-interacting system. Here, we find some relations in this non-interacting system, which can enable us to set up the thermodynamical relations for a neutral electron-nucleus mixture in terms of quantities of the non-interacting system and the exchange-correlation effect. In this way, Andersen’s force theorems are clearly described and easily proved in conjunction with other types of force theorems, Janak’s theorem extended to a finite-temperature system, pressure formulas and some thermodynamical relations. For this purpose, thermodynamics in the DF theory is presented in a systematic and explicit way. The density-functional (DF) theory has been used with success to investigate the equilibrium properties of solids and liquid metals in the almost cases when the electrons can be treated as being in a perfectly degenerate state. Therefore, not so much attention is paid to thermodynamics in the DF theory, although the DF theory