In statistical mechanics and thermodynamics the compressibility equation refers to an equation which relates the isothermal compressibility is the number density, g(r) is the radial distribution function 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.

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