To develop a formalism for the statistical thermodynamics of non-uniform fluids functional differentiation was used extensively by Percus and Lebowitz (1961), which led to the Percus–Yevick equation linking the density distribution function and the direct correlation. Other closure relations were also proposed;the Classical-map hypernetted-chain method, the BBGKY hierarchy. In the late 1970s classical DFT was applied to the liquid–vapor interface and the calculation of surface tension. Other applications followed: the freezing of simple fluids, formation of the glass phase, the crystal–melt interface and dislocation in crystals, properties of polymer systems, and liquid crystal ordering. Classical DFT was applied to colloid dispersions, which were discovered to be good models for atomic systems. By assuming local chemical equilibrium and using the local chemical potential of the fluid from DFT as the driving force in fluid transport equations, equilibrium DFT is extended to describe non-equilibrium phenomena and fluid dynamics on small scales.