  We develop a general analysis of the diffusive dynamics of polydisperse
polymers in the presence of chemical potential gradients, within the context of
the tube model (with all species entangled). We obtain a set of coupled
dynamical equations for the time evolution of the polymeric densities with
explicitly derived coefficients. For the case of chemical polydispersity (a set
of chains that are identical except for having a continuous spectrum of
enthalpic interaction strengths) the coupled equations can be fully solved in
certain cases. For these we study the linearised mode spectrum following a
quench through the spinodal, with and without a passive (polymeric) solvent. We
also study the more conventional case of length polydisperse chains in a poor
solvent.
