  The quasi--equilibrium or maximum entropy approximation is applied in order
to derive constitutive equations from kinetic models of polymer dynamics. It is
shown in general and illustrated for an example how canonical distribution
functions are obtained from the maximum entropy principle, how macroscopic and
constitutive equations are derived therefrom and how these constitutive
equations can be implemented numerically. In addition, a measure for the
accuracy of the quasi--equilibrium approximation is proposed that can be
evaluated while integrating the constitutive equations. In the example
considered, it is confirmed that the accuracy of the approximation is increased
by including more macroscopic variables. In steady elongational flow, it is
found that more macroscopic variables need to be included above the
coil--stretch transition to achieve the same accuracy as below.
