  Starting with a micropolar formulation, known to account for nonlocal
microstructural effects at the continuum level, a generalized Langevin equation
(GLE) for a particle, describing the predominant motion of a localized region
through a single displacement degree-of-freedom (DOF), is derived. The GLE
features a memory dependent multiplicative or internal noise, which appears
upon recognising that the micro-rotation variables possess randomness owing to
an uncertainty principle. Unlike its classical version, the new GLE
qualitatively reproduces the experimentally measured fluctuations in the
steady-state mean square displacement of scattering centers in a polyvinyl
alcohol slab. The origin of the fluctuations is traced to nonlocal spatial
interactions within the continuum. A constraint equation, similar to a
fluctuation dissipation theorem (FDT), is shown to statistically relate the
internal noise to the other parameters in the GLE.
