  Linear polymers and other connected "line liquids" exhibit a coupling between
density and equilibrium nematic order on the macroscopic level that gives rise
to a Meyer-de Gennes vectorial conservation law. Nevertheless, isotropic linear
polymer melts/solutions exhibit fluctuations of the density and of the nematic
order that are not coupled by this vectorial constraint, just like for
isotropic liquids composed of disconnected non-spherical particles. It takes
the proper tensorial description of the nematic order in linear polymer
liquids, leading to a tensorial conservation law connecting density and
orientational order, that finally implicates coupled density and nematic order
fluctuations, already in the isotropic system and not subject to the existence
of an orientational phase transition. This coupling implies that a spatial
variation of density or a local concentration gradient will induce nematic
order and thereby an acoustic or osmotic optical birefringence even in an
otherwise isotropic polymer melt/solution. We validate the theoretical
conceptions by performing detailed Monte Carlo simulations of isotropic melts
of "soft" worm-like chains with variable length and flexibility, and comparing
the numerically determined orientation correlation functions with predictions
of the macroscopic theory. The methodology drawn sets forth a means of
determining the macroscopic parameters by microscopic simulations to yield
realistic continuum models of specific polymeric materials.
