Hydrodynamics and Collective Angular-Momentum Fluctuations in Molecular Fluids

Abstract

Generalized hydrodynamics for classical fluids composed of structured molecules is discussed from a fundamental microscopic viewpoint. The analysis is concentrated on collective fluctuations of the intrinsic molecular angular momentum, and their coupling to the conserved densities of particle number, linear momentum, and energy. It is found from symmetry that the transverse components of linear and angular momentum are dynamically coupled, while the longitudinal angular momentum density moves independently of the other variables. By using the Zwanzig-Mori projection-operator technique, we derive closed and rigorous equations of motion for the set of fluctuations considered. For the case where the intrinsic angular momentum is not far from being separately conserved, approximations can be motivated which reduce these equations to simple relaxation equations, valid for small $k$ and long times. General, Kubo-type expressions for the relaxation coefficients are given. Finally, sum-rule considerations are presented from which these coefficients can be approximately calculated.