  Reformulating constitutive relation in terms of gradient dynamics (being
derivative of a dissipation potential) brings additional information on
stability, metastability and instability of the dynamics with respect to
perturbations of the constitutive relation, called CR-stability. CR-instability
is connected to the loss of convexity of the dissipation potential, which makes
the Legendre-conjugate dissipation potential multivalued and causes dissipative
phase transitions, that are not induced by non-convexity of free energy, but by
non-convexity of the dissipation potential. CR-stability of the constitutive
relation with respect to perturbations is then manifested by constructing
evolution equations for the perturbations in a thermodynamically sound way. As
a result, interesting experimental observations of behavior of complex fluids
under shear flow and supercritical boiling curve can be explained.
