On the relationship between pairwise fluctuations and thermodynamic derivatives

General expressions are derived for the pairwise fluctuations of thermodynamic properties in multicomponent systems, in terms of thermodynamic derivatives. The expressions are valid for an open system close to thermodynamic equilibrium in contact with an energy and mass reservoir. The system is defined by an arbitrary extensive constraint. Fluctuations involving the entropy S, the volume V, and the number of molecules Ni of each component, as well as their conjugate variables, are expressed as second‐order derivatives of the energy U and Legendre‐transformed functions. Fluctuations involving U itself are obtained in the entropy representation of the fundamental equation.