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Dynamic Density Functional Theory (DDFT)



Dynamic density functional theory (DDFT) is, on the one hand, a time-dependent (dynamic) extension of the static density functional theory (DFT) and, on the other hand, the generalization of Fick's law to the diffusion of interacting particles. The time evolution of the ensemble-averaged density of Brownian particles is given as an integrodifferential equation in terms of the equilibrium Helmholtz free energy functional (or the grand canonical functional). DDFT resolves density variations on length scales down to the particle size but only works for slow relaxing dynamics close to equilibrium.


One can prove that in thermal equilibrium, in a grand canonical ensemble (i.e., volume, chemical potential, and temperature are fixed), the grand canonical free energy Ω(ρ(r)) of a system can be written as a functional of the one-body density ρ(r) alone, which will depend