  We derive a thermodynamically consistent framework for incorporating
entanglement dynamics into constitutive equations for flowing polymer melts. We
use this to combine the convected constraint release (CCR) dynamics of
Ianniruberto-Marriccui into a finitely-extensible version of the Rolie-Poly
model, and also include an anisotropic mobility as in the Giesekus model. The
reversible dynamics are obtained from a free energy that describes both a
finitely-extensible conformation tensor and an ideal gas of entanglements along
the chain. The dissipative dynamics give rise to coupled kinetic equations for
the conformation tensor and entanglements, whose coupling terms describe
shear-induced disentanglement. The relaxation dynamics of the conformation
tensor follow the GLaMM and Rolie-Poly models, and account for reptation,
retraction and CCR. We propose that the relaxation time $\tau_\nu$ for
entanglement recovery is proportional to the Rouse time $\tau_R$ which governs
polymer stretch within the tube. This which matches recent molecular dynamics
simulations, and corresponds to relaxing the entanglement number before the
entire polymer anisotropy has relaxed on the longer reptation time $\tau_d$.
Our model suggests that claimed signatures of slow re-entanglement on the
reptation time in step-strain experiments may be interpreted as arising from
anisotropies in reptation dynamics.
