Ergodicity breaking in well-behaved generalized Langevin equations

By means of the concepts of dissipative stability and stochastic realizability, the phenomenon of ergodicity breaking observed in Generalized Langevin Equations (GLEs) in the presence of nonvanishing friction factors [Phys. Rev. E 83, 062102 (2011)] can be properly explained: it occurs at the boundary of the region of dissipative stability; in those cases, this region coincides with that of stochastic realizability. This is the case of the Plyukhin model that considers a generalized Debye kernel. In the presence of dissipative kernels characterized by real-valued relaxation rates corresponding to the rheological behavior of viscoelastic fluids, since the domain of stochastic realizability is strictly contained within the region of dissipative stability, this phenomenon cannot be observed if Kubo's theory of fluctuation-dissipation holds. The hydromechanic theory of GLEs also provides a physical interpretation of the ergodicity breaking reported by [Chin. Phys. Lett. 22, 1845 (2005)] that stems from a dissipationless ‘'fluid-inertial” effect, leading to superdiffusion.