Onsager Relations and the Spectrum of Critical Opalescence

The necessity of extending the hydrodynamic equations near the critical point is investigated on the basis of Onsager's assumption concerning the regression of fluctuations. It is shown that it follows from the Onsager relations that in general the new equations are nonlocal. The most important coefficient corresponding to the inverse compressibility in the original equations is obtained from the Onsager relations and expressed in terms of the equilibrium pair correlation function. Fixman's extension of hydrodynamics follows when the pair correlation is given by the Ornstein—Zernike formula. The consequences for the spectrum of light scattering near the critical point are studied and the width and relative intensity of the central scattering peak are expressed in terms of the equilibrium pair correlation function.