Is there a need for an extended phase definition for systems far from equilibrium?

Abstract Phase diagrams out of equilibrium have been the subject of intense research. An essential concept in these diagrams is the phase definition. Currently, that definition is well established for systems at classic thermodynamic equilibrium conditions. However, such phase definition is inadequate for systems that are not at equilibrium in the classic thermodynamic sense, like fluid systems under flowing conditions. Complex fluids may exhibit instabilities like shear-banding flow and a non-equilibrium critical point where banding flow ends. At this point, the fluid undergoes a phase transition from heterogeneous to homogeneous states. An extended thermodynamic space of variables is considered to adequately address this situation, which includes non-conservative variables such as stress and shear rate. Hence, the current phase definition based on conservative variables does not apply to non-equilibrium phase diagrams. On this basis, a broader definition of phase is required. We propose that this broader definition considers the thermodynamic variables space of Extended Irreversible Thermodynamics and the mathematical conditions that ensure compatibility between equilibrium and non-equilibrium conditions for systems where phases are well described by thermodynamic potentials even out of equilibrium.