Nonlocal Hydrodynamic Equations and the Spectrum of Critical Opalescence

Abstract

Both the thermodynamic theory of fluctuations and the linearized hydrodynamics equations are modified in order to take into account nonlocal effects. The description is based on the assumption that the entropy of the system is a functional of the energy and number density which can be expanded in a functional Taylor series about the homogeneous equilibrium state. In this way the well-known difficulties which arise with the “local functional expansion” of the semithermodynamic method are avoided. The modifications to be expected in the Landau–Placzek theory for the spectrum of critical opalescence are investigated. In particular, the angle or k dependence of the sound velocity, the Landau–Placzek ratio, and the width of the central component are discussed.