Nonergodic Brownian Dynamics and the Fluctuation-Dissipation Theorem
  Nonergodic Brownian motion is elucidated within the framework of the generalized Langevin equation. For thermal noise yielding either a vanishing or a divergent zero-frequency friction strength, the non-Markovian Browninan dynamics exhibits a riveting, anomalous diffusion behavior being characterized by a ballistic or possibly also a localized dynamics. As a consequence, such tailored thermal noise may cause a net acceleration of directed transport in a rocking Brownian motor. Two notable conditions for the thermal noise are identified in order to guarantee the fluctuation-dissipation theorem of first kind. 
Jing-Dong Bao, Yi-Zhong Zhuo, Fernando A. Oliveira and Peter H\"anggi