  We have performed non-equilibrium dynamics simulations of a binary
Lennard-Jones mixture in which an external force is applied on a single tagged
particle. For the diffusive properties of this particle parallel to the force
superdiffusive behavior at intermediate times as well as giant long-time
diffusivity is observed. A quantitative description of this non-trivial
behavior is given by a continuous time random walk analysis of the system in
configuration space. We further demonstrate, that the same physical properties
which are responsible for the superdiffusivity in non-equilibrium systems also
determine the non-Gaussian parameter in equilibrium systems.
