  We present a new strategy for introducing population balances into full-chain
constitutive models of living polymers with linear chain architectures. We
provide equations to describe a range of stress relaxation processes covering
both unentangled systems (Rouse-like motion) and well entangled systems
(reptation, contour length fluctuations, chain retraction, and constraint
release). Special attention is given to the solutions that emerge when the
'breaking time' of the chain becomes fast compared to various stress relaxation
processes. In these 'fast breaking' limits, we reproduce previously known
results (with some corrections) and also present new results for nonlinear
stress relaxation dynamics. Our analysis culminates with a fully developed
constitutive model for the fast breaking regime in which stress relaxation is
dominated by contour length fluctuations. Linear and nonlinear rheology
predictions of the model are presented and discussed.
