Statistical properties of a tangentially driven active filament

Active polymers play a central role in many biological systems, from bacterial flagella to cellular cytoskeletons. Minimal models of semiflexible active filaments have been used to study a variety of interesting phenomena in active systems, such as defect dynamics in active nematics, clustering and laning in motility assays, and conformational properties of chromatin in eukaryotic cells. In this paper, we map a semiflexible polymer to an exactly solvable active Rouse chain, which enables us to analytically compute configurational and dynamical properties of active polymers with arbitrary rigidity. Upon mapping back to the semiflexible filament, we see that the center of mass diffusion coefficient grows linearly with an activity parameter that is renormalized by the polymer persistence length. These results closely agree with numerical data obtained from microscopic simulations. (paper: classical statistical mechanics, equilibrium and non-equilibrium)