A novel approach to the description of entangled polymeric liquids has recently been presented [E Greco, Phys. Rev. Lett. 88, 108301 (2002)], where the mechanical behavior of any subchain connecting two entanglements is determined through the grand canonical formalism of statistical mechanics, thus properly allowing for exchange of particles (Kuhn segments) among subchains. The deduction of a strain measure tensor in this new approach is given and discussed in detail. It is also shown that the new strain measure tensor fulfills the stress-optical law. Predictions obtained with this strain measure are compared with data for step-strain deformations both in shear and elongation, and good agreement is found. The normal stress ratio in step shear is found to be better described here than with the classical "rigorous" Doi-Edwards strain measure. (C) 2003 The Society of Rheology.