Compressibility equation

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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.


  1. J. S. Rowlinson "The equation of state of dense systems", Reports on Progress in Physics 28 pp. 169-199 (1965)