Nonequilibrium thermodynamics of the soft glassy rheology model

The soft glassy rheology (SGR) model is a mesoscopic framework which proved to be very successful in describing flow and deformation of various amorphous materials phenomenologically (e.g., pastes, slurries, foams, etc.). In this paper, we cast SGR in a general, model-independent framework for nonequilibrium thermodynamics called general equation for the nonequilibrium reversible-irreversible coupling. This leads to a formulation of SGR which clarifies how it can properly be coupled to hydrodynamic fields, resulting in a thermodynamically consistent, local, continuum version of SGR. Additionally, we find that compliance with thermodynamics imposes the existence of a modification to the stress tensor as predicted by SGR.