  The classical Density Functional Theory (DFT) is introduced as an application
of entropic inference for inhomogeneous fluids at thermal equilibrium. It is
shown that entropic inference reproduces the variational principle of DFT when
information about expected density of particles is imposed. This process
introduces an intermediate family of trial density-parametrized probability
distributions, and consequently an intermediate entropy, from which the
preferred one is found using the method of Maximum Entropy (MaxEnt). As an
application, the DFT model for slowly varying density is provided, and its
approximation scheme is discussed.
