Compounding Formula Approach to Chromatin and Active Polymer Dynamics

Active polymers are ubiquitous in nature, and often kicked by persistent noises that break detailed balance. In order to capture the out-of-equilibrium dynamics of such active polymers, we propose a simple yet reliable analytical framework based on a compounding formula. Connecting polymeric dynamics to the isolated monomeric behavior via the notion of tension propagation, the formula allows us to clarify rich scaling scenarios alongside corresponding intuitive physical pictures. We demonstrate distinctive transient and steady-state scalings due to the non-Markovian nature of the active noise. Aside from a paradigmatic example of an active Rouse polymer, we expect the framework to be applicable to wide variety of spatially extended systems, including more general polymers (crumpled globule, semiflexible polymers, etc.), fluctuation of growing interfaces, and an array of particles in single-file configuration.