Simple Non-equilibrium Thermodynamics Applications to Polymer Rheology

We review here recent developments in non-equilibrium thermodynamics and their applications to rheology. In particular we review the application of the dissipative Hamiltonian formalism to incompressible, homogeneous and isothermal flows of flexible polymer systems. We show not only the advantages that have been brought up by the nonequilibrium thermodynamics approach but also exactly where the actual contributions are in combination from a variety of specific modeling examples ranging from simple, one-conformation models to most recent coupled multivariable examples. In all cases, special attention is paid to convey the physical significance of the models through a close association to a more detailed microscopic interpretation.