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 pf 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.