Physics of active polymers: scaling analysis via a compounding formula

TL;DR

This paper introduces a transparent scaling theory for active polymers, expressing monomer dynamics as a combination of isolated active particle behavior and connectivity effects, providing new insights into non-equilibrium polymer behavior.

Contribution

The work develops a novel scaling framework that isolates activity effects from connectivity, enabling simplified analysis of active polymer dynamics beyond traditional models.

Findings

Scaling predictions match exact calculations across models

Framework captures emergent dynamical regimes

Robust across diverse noise statistics

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.