Physics of active polymers: scaling analysis via a compounding formula

Abstract

Active polymeric systems exhibit a rich spectrum of non-equilibrium phenomena arising from stochastic forces that explicitly break detailed balance. Despite the rapid growth of experimental and numerical studies, analytical progress remains limited. To date, theoretical understanding relies largely on variants of the active Rouse model, whose formal solutions, though exact, are often obscured by summations over Rouse modes and therefore provide limited direct physical insight. In this work, we develop a transparent scaling theory that captures the tagged-monomer mean-squared displacement (MSD) in active polymers through a compounding formula: the MSD of a monomer in the chain is expressed as that of an isolated active particle, modulated by a connectivity factor encoding tension propagation along the polymer backbone. This approach isolates the role of activity from that of polymer connectivity and reveals the emergent dynamical regimes in a physically intuitive manner. We test the scaling predictions against exact calculations for a broad class of generalized active polymer models driven by diverse noise statistics. The agreement demonstrates the robustness of the scaling framework across microscopic details. Our results provide a simple and extensible theoretical structure that can be applied to complex and analytically intractable active polymer systems, thereby offering a unifying perspective on non-equilibrium polymer dynamics.