Signatures of irreversibility in the fluctuation statistics of spatially extended noise-driven systems

Nature abounds with instances of spatially extended dissipative dynamical systems that are driven by both thermal equilibrium noise and non-equilibrium (e.g., active) sources. The recently introduced concept of an irreversibility tensor field [1] provides a useful metric for quantifying the relative roles of equilibrium and non-equilibrium noise sources. It also allows the characterization of dissipative spatial structures that emerge in response to the fluctuations that drive them. Here we focus on the overdamped fluctuation statistics of one-dimensional elastic filaments with rigidity (e.g., rods) driven by localized active forces as well as thermal noise. Such systems describe dynamics of filamentary structures embedded in cytoskeletal networks that contain active sources such as localized molecular motors. A generalized fluctuation-dissipation relation is presented which takes the form of a two-dimensional boundary value problem for the spatial correlation field of filament displacements. The irreversibility field is determined from the correlation field; observed spatial patterns reflect both the spatial placement and footprint of noise sources as well as the elastic properties of the filament.

[1] J. C. Neu and S. W. Teitsworth, arXiv:2403.10728 (2024).