Deciphering the Manifestations of Topological Imprints in Low-Entangled Polymer

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.