Thermodynamic derivatives of correlation functions

Abstract

General expressions are derived for the thermodynamic derivatives of a property <Q>, where Q is a function (static or time-dependent) of the phase variables and <…> is an average over an equilibrium grand canonical ensemble. As an example of the use of these expressions we then consider the case where <Q> is a time-dependent density-density correlation function. Thermodynamic derivatives of the time-dependent Van Hove correlation functions are considered in detail, and examples of how the resulting expressions can be used to interpret neutron-scattering data are given. The expressions developed lead to more stringent ways of testing theories of fluids, and provide a method for studying triplet correlation functions which have been nearly inaccessible in the past. We expect the general relationships to prove equally useful when applied to other experimental methods for studying time-correlation functions (e.g. absorption or scattering of electromagnetic radiation, relaxation phenomena).