Irreversible dynamics of a filament embedded in a noisy viscoelastic medium

This talk focuses on the overdamped fluctuation statistics of elastic filaments (e.g., strings or rods) driven by active forces which induce irreversibility. Such systems occur in a range of contexts and include, for example, biophysical systems such as artificial or natural filamentary structures embedded in cytoskeletal networks including the effects of localized molecular motors. We translate the traditional statistical mechanics of normal modes into direct spatial statistics which allows discernment of the spatial structure of dissipation and fluctuational work done by the active forces. We introduce a generalization of stochastic area as a tensor field and a closely related concept of an irreversibility field. These quantities both serve as useful metrics of irreversibility in spatially extended systems. We also carry out a mapping from force statistics to filament statistics which leads to a generalization of the fluctuation-dissipation relation. To illustrate general results, we construct explicit two-dimensional plots of the tensor components in the discrete plane of mode pairs of a tensioned elastic string between fixed endpoints. These maps show clear dependence on properties of the embedding medium as well as the temporal statistics and spatial support of the noisy active forces. In particular, we can discern how highly localized fluctuational forces lead to dissipation on larger length scales associated with long wavelength modes.