Deciphering the Manifestations of Topological Imprints in Low-Entangled Polymer

Abstract Entanglements are topological constraints governing the nonequilibrium statistical mechanics, nonlinear dynamics and ultimate performance of polymers. By breaking topological ergodicity during synthesis, via concurrent polymerization and crystallization, single-site catalysis provides a testbed to engineer nonequilibrium chain topologies. How these catalyst-imprinted architectures evolve toward topological equilibrium represents one of the most compelling frontiers in polymer physics. In this Viewpoint, we demonstrate that topological nonequilibrium cannot be collapsed to a single volume averaged observable. Instead, it manifests like a multiscale symphony, where local contacts, spatial density fluctuations, interphase entropic barriers and nonlinear stress-transmitting networks evolve simultaneously. We build upon decades of foundational breakthroughs and unify these complementary physical observations to turn an inefficient debate into a predictive paradigm, encouraging exciting frontiers for nonequilibrium polymer physics and solvent-free processing.