  We study anomalous diffusion for one-dimensional systems described by a
generalized Langevin equation. We show that superdiffusion can be classified in
normal superdiffusion and fast superdiffusion. For fast superdiffusion, we
prove that the Fluctuation-Dissipation Theorem does not hold, which induces an
effective temperature in the system. This effective temperature is a signature
of metastability found in many complex system such as Spin-Glass and granular
material.
