  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.
