Extended irreversible thermodynamics and its relation with other continuum approaches

We present an introduction to extended irreversible thermodynamics (EIT) as applied to polymer solutions in the presence of shear flow and of diffusion flux. We discuss with special attention the definition of chemical potential in non-equilibrium situations and its use in the analysis of shear-induced phase transitions. In the second part, we compare EIT with other contemporary continuum approaches: theories with internal variables, the GENERIC approach, and the matrix model. All these theories share an emphasis on the relations between dynamics and thermodynamics at a deeper level than in the classical theory, but each of them has some peculiar advantage in the analysis of some specific aspects of physical problems.