# Compressibility equation

The **compressibility equation** () can be derived from the density fluctuations of the grand canonical ensemble (Eq. 3.16 in Ref. 1). For a homogeneous system:

where is the pressure, is the temperature, is the total correlation function, is the pair distribution function and is the Boltzmann constant.

For a spherical potential

Note that the compressibility equation, unlike the energy and pressure equations, is valid even when the inter-particle forces are not pairwise additive.