The Fluctuation-Dissipation Theorem fails for fast superdiffusion

Abstract

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