<![CDATA[Abstract In this brief article, the extension of density functional theory for non-equilibrium systems is presented. Density functional theory is a powerful framework in order to study the static properties of electronic systems via a variational principle whereby the density (varies in 3 dimension space) holds a key role instead of the many-body wave function. Evans (Adv. Phys., 1979) fully realized the importance of this and extended the theory for inhomogeneous fluid systems. Then in an urgent need to extend the theory for dynamical equilibrium or non-equilibrium systems, comes dynamical density functional theory. Here, the idea behind dynamical density functional theory is given based on the Smoluchowski equation. Keywords: density functional theory, non-equilibrium systems, variational principle, Smoluchowski equation]]>
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