Irreversible dynamics of a continuum driven by active matter

We study the fluctuational behavior of overdamped elastic filaments (e.g., strings or rods) driven by active matter which induces irreversibility. The statistics of discrete normal modes are translated into the continuum of the position representation which allows discernment of the spatial structure of dissipation and fluctuational work done by the active forces. The mapping of force statistics onto filament statistics leads to a generalized fluctuation-dissipation relation which predicts the components of the stochastic area tensor and its spatial proxy, the irreversibility field. We illustrate the general theory with explicit results for a tensioned string between two fixed endpoints. Plots of the stochastic area tensor components in the discrete plane of mode pairs reveal how the active forces induce spatial correlations of displacement along the filament. The irreversibility field provides additional quantitative insight into the relative spatial distributions of fluctuational work and dissipative response.