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We use Brownian dynamics simulations and advanced topological profilingmethods to characterize the out-of-equilibrium evolution of self-entanglementin linear polymers confined into nano-channels and under periodic compression.We distinguish two main forms of entanglement, geometrical and topological. Thelatter is measured by the number of (essential) crossings of the physical knotdetected after a suitable bridging of the chain termini. The former is insteadmeasured as the average number of times a linear chain appears to cross itselfwhen viewed under all projections, and is irrespective of the physical knottedstate. The key discovery of our work is that these two forms of entanglementare uncoupled and evolve with distinct dynamics. While geometrical entanglementis typically in phase with the compression-elongation cycles and it isprimarily sensitive to its force f, the topological measure is mildly sensitiveto cyclic modulation but strongly depends on both compression force f andduration k. The findings could assist the interpretation of experiments usingfluorescence molecular tracers to track physical knots in polymers.Furthermore, we identify optimal regions in the experimentally-controllableparameter space in which to obtain more/less topological and geometricalentanglement; this may help designing polymers with targeted topology.

Separation of Geometrical and Topological Entanglement in Confined Polymers Driven Out-Of-Equilibrium