  Many cytoskeletal biopolymers are "active," consuming energy in large
quantities. In this Letter, we identify a fundamental difference between active
polymers and passive, equilibrium polymers: for equal mean lengths, active
polymers can reorganize faster than equilibrium polymers. We show that
equilibrium polymers are intrinsically limited to linear scaling between mean
lifetime and mean length, MFPT ~ <L>, by analogy to 1-d Potts models. By
contrast, we present a simple active-polymer model that improves upon this
scaling, such that MFPT ~ <L>^{1/2}. Since to be biologically useful,
structural biopolymers must typically be many monomers long, yet respond
dynamically to the needs of the cell, the difference in reorganization kinetics
may help to justify active polymers' greater energy cost. PACS numbers:
87.10.Ed, 87.16.ad, 87.16.Ln
