Resolving vibrational and structural contributions to isothermal compressibility

The well-known and general "compressibility theorem" for pure substances relates κ_T =-(∂lnV/∂p)_N,T to a spatial integral involving the pair correlation function g⁽²⁾. The isochoric inherent structure formalism for condensed phases separates g⁽²⁾ into two fundamentally distinct contributions: a generally anharmonic vibrational part, and a structural relaxation part. Only the former determines κ_T for low-temperature crystals, but both operate in the liquid phase. As a supercooled liquid passes downward in temperature through a glass transition, the structural contribution to κ_T switches off to produce the experimentally familiar drop in this quantity. The Kirkwood-Buff solution theory forms the starting point for extension to mixtures, with electroneutrality conditions creating simplifications in the case of ionic systems.