Thermodynamics of Non-Uniform Systems and Density Functional Theory

Abstract

The relationship of the thermodynamics for non-uniform systems and density functional theory is reviewed. It is observed that the relevant universal functionals are the same in both cases under appropriate conditions for thermodynamics. The variational context arises from the convexity properties of the functionals as represented by equilibrium statistical mechanics. Within thermodynamics a choice of local density or local chemical potential for the local variable can be made. In the latter case a “dual” form for density functional theory applies (“potential functional” theory). The special case of electrons and ions is considered, and the important condition of charge neutrality for thermodynamics is noted. These general results are extended to include the interatomic pair potential as an independent variable. Its conjugate is the equilibrium pair correlation function. As an application, the construction of a classical system to represent a given quantum system in terms of effective potentials is shown to result from the Euler equations of this extended variational formulation.