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, the thermodynamics in the DF theory is presented in a systematic and explicit way.