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In statistical mechanics and thermodynamics the compressibility equation refers to an equation which relates the isothermal compressibility to the structure of the liquid. It reads:
k T = 1 + ρ ∫ V d r − 1 ] {\displaystyle kT\left=1+\rho \int _{V}\mathrm {d} \mathbf {r} -1]}
where ρ {\displaystyle \rho } is the number density, g is the radial distribution function and k T {\displaystyle kT\left} is the isothermal compressibility.
Using the Fourier representation of the Ornstein-Zernike equation the compressibility equation can be rewritten in the form:
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