  Closure seems to be something rheologists would prefer to avoid. Here, the
story of closure is told in such a way that one should enduringly forget any
improper undertone of "uncontrolled approximation" or "necessary evil" which
might arise, for example, in reducing a diffusion equation in configuration
space to moment equations. In its widest sense, closure is associated with the
search for self-contained levels of description on which time-evolution
equations can be formulated in a closed, or autonomous, form. Proper closure
requires the identification of the relevant structural variables participating
in the dominant processes in a system of interest, and closure hence is
synonymous with focusing on the essence of a problem and consequently with deep
understanding. The derivation of closed equations may or may not be accompanied
by the elimination of fast processes in favor of dissipation. As a general
requirement, any closed set of evolution equations should be thermodynamically
admissible. Thermodynamic admissibility comprises much more than the second law
of thermodynamics, most notably, a clear separation of reversible and
irreversible effects and a profound geometric structure of the reversible terms
as a hallmark of reversibility. We discuss some implications of the intimate
relationship between nonequilibrium thermodynamics and the principles of
closure for rheology, and we illustrate the abstract ideas for the rod model of
liquid crystal polymers, bead-spring models of dilute polymer solutions, and
the reptation model of melts of entangled linear polymers.
