Incompressibility and the symmetry of pressure-fluctuation correlations in polymeric liquids

We point out that, under the incompressibility constraint, the two-time pressure-fluctuation correlator of polymeric liquids becomes an isotropic, symmetric, and pair-index-traceless fourth-rank tensor. As a consequence, the self- and cross correlations of normal pressure fluctuations are strictly proportional to the shear pressure correlation, with universal prefactors of 4/3 and -2/3, respectively, for equilibrium dynamics in the long-time limit. By contrast, this symmetry structure is violated in a broad class of polymer models, including the Rouse and slip-link models, which predict incorrect relative weights between normal pressure-fluctuation correlations and shear pressure correlation. This observation suggests that the pressure tensor generated by these models must be projected onto the traceless symmetric subspace to recover hydrodynamically consistent behavior.