  Understanding how entanglements affect the behaviour of polymeric complex
fluids is an open challenge in many fields. To elucidate the nature and
consequence of entanglements in dense polymer solutions, we propose a novel
method: a "dynamical entanglement analysis" (DEA) to extract spatio-temporal
entanglement structures from the pair-wise displacement correlation of
entangled chains. By applying this method to large-scale Molecular Dynamics
simulations of linear and unknotted, nonconcatenated ring polymers, we find a
strong and unexpected cooperative dynamics: the footprint of mutual entrainment
between entangled chains. We show that DEA is a powerful and sensitive probe
that reveals previously unnoticed, and architecture-dependent, spatio-temporal
structures of dynamical entanglement in polymeric solutions. We also propose a
mean-field approximation of our analysis which provides previously
under-appreciated physical insights into the dynamics of generic entangled
polymers. We envisage DEA will be useful to analyse the dynamical evolution of
entanglements in generic polymeric systems such as blends and composites.
