Wavelength-dependent fluctuations in classical fluids: I. The long wavelength limit

A discussion is given of the properties of correlation functions for wavelength-dependent fluctuations of density, energy, stress, etc. in a classical fluid. Three separate but related topics are treated: (i) the definition and properties of the correlation functions - in particular the consequences of the condition that they be stationary in time, (ii) the long wavelength limit, where expressions for thermodynamic derivatives are obtained from the correlation functions in terms of s-particle distribution functions and (iii) the definition of κ-dependent elastic moduli in a fluid. In an appendix it is shown that the results of (ii) are in accord with those derived from the equilibrium grand canonical ensemble.