The pompon model for branched polymers is re-formulated within a general fr
amework of nonequilibrium thermodynamics. While the original model of McLei
sh and Larson is found to be thermodynamically admissible, nonequilibrium t
hermodynamics strongly suggests several model modifications. As an immediat
e consequence, a nonzero second normal-stress coefficient in shear flow is
predicted by the modified pompon model.