Dynamics and thermodynamics of complex fluids.  II. Illustrations of a general formalism

For a number of well-known time-evolution equations for nonequilibrium systems we extract a common structure from these equations, referred to as a general equation for the nonequilibrium reversible-irreversible coupling (GENERIC). This fundamental structure is determined by four building blocks, two ``potentials'' (total energy and entropy) and two ``matrices.'' We illustrate for various examples how three of the four building blocks can be determined in a rather straightforward manner so that, within our GENERIC approach to nonequilibrium dynamics, understanding of a given nonequilibrium system is reduced to determining a single ``metric matrix,'' or friction matrix, either empirically or by more microscopic considerations. In formulating nonisothermal polymer kinetic theories, we show how the general structure provides a clear distinction between spring potentials of energetic and entropic origins in the various time-evolution equations.