ON THE RELATIONSHIPS BETWEEN THERMODYNAMIC FORMALISMS FOR COMPLEX FLUIDS

In recent years, several seemingly distinct approaches have been devel oped which aim to describe the mechanics and thermodynamics of complex fluids under dynamical conditions. Two of these approaches of decided ly different flavor are the Matrix Model of thermodynamically driven s ystems developed by Jongschaap and the GENERIC formalism of Grmela and Ottinger. Herein, we examine the interrelationships between these two alternate approaches on an abstract level and work out direct connect ions for two specific examples of thermodynamically driven systems: a gas housed in a cylinder closed by a piston subject to external force and potential fields, and a dilute solution of Hookean dumbbells in a Bow field. It is demonstrated that the Matrix Model derives from the G ENERIC formalism when the global thermodynamic system is split into tw o parts: a smaller open thermodynamic system with fewer internal varia bles, and its environment composed of external driving forces which ar e determined from the variables which are neglected in the smaller sys tem. Thus the Matrix Model provides an explicit answer to the question of how to handle driven systems within the more global GENERIC formal ism. It is also shown that the Matrix Model requires a prerequisite kn owledge of the laws of motion for a given system, whereas these are ex plicitly embedded in the GENERIC structure.