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Based on the generalized Langevin equation for the momentum of a Brownianparticle a generalized asymptotic Einstein relation is derived. It agrees withthe well-known Einstein relation in the case of normal diffusion but continuesto hold for sub- and super-diffusive spreading of the Brownian particle's meansquare displacement. The generalized asymptotic Einstein relation is used toanalyze data obtained from molecular dynamics simulations of a two-dimensionalsoft disk fluid. We mainly concentrated on medium densities for which we foundsuper-diffusive behavior of a tagged fluid particle. At higher densities arange of normal diffusion can be identified. The motion presumably changes tosub-diffusion for even higher densities.

Normal versus anomalous self-diffusion in two-dimensional fluids: Memory function approach and generalized asymptotic Einstein relation