Entropic Density Functional Theory

A formulation of the density functional theory is constructed on the foundations of entropic inference. The theory is introduced as an application of maximum entropy for inhomogeneous fluids in thermal equilibrium. It is shown that entropic inference produces the variational principle of DFT when information about the expected density of particles is imposed. This process introduces a family of trial density-parametrized density matrices from which the preferred density matrix is found using the method of quantum maximum entropy. As illustrations some known approximation schemes of the theory are discussed.