In statistical mechanics and thermodynamics the compressibility equation refers to an equation which relates the isothermal compressibility (and indirectly the pressure) to the structure of the liquid. It reads:
where is the number density, g(r) is the radial distribution function and is the isothermal compressibility.
Using the Fourier representation of the Ornstein-Zernike equation the compressibility equation can be rewritten in the form:
where h(r) and c(r) are the indirect and direct correlation functions respectively. The compressibility equation is one of the many integral equations in statistical mechanics.