Subdiffusive transport close to thermal equilibrium: From the Langevin equation to fractional diffusion

Subdiffusion in the presence or absence of an external force field is estab lished on the basis of an extension of conventional Langevin dynamics to in clude long-tailed trapping events. It is demonstrated how the presence of t he trapping events leads to the macroscopic observation of fractional diffu sion, described by a fractional Klein-Kramers equation.