General projection operator formalism for the dynamics and thermodynamics of complex fluids

By applying the projection operator method, we derive the g̱eneral e̱quation for the ṉone̱quilibrium reversible-irreversible coupling (GENERIC) that, in previous work [Phys. Rev. E 56, 6620 (1997); 56, 6633 (1997)], was obtained by empirical arguments. We find microscopic expressions for the building blocks of GENERIC, and we generally derive the rules for passing from any given level of description to a more macroscopic one.