Pair distribution function

For a fluid of $N$ particles, enclosed in a volume $V$ at a given temperature $T$ (canonical ensemble) interacting via the `central' potential $\mathrm{\Phi }(r)$, the two particle distribution function is defined as

${\mathrm{g}}_N^{(2)}(r_1,r_2)=V^2\frac{\int ...\int e^{-\beta \mathrm{\Phi }(r_1,...,r_N)}\mathrm{d}{r}_3...\mathrm{d}{r}_N}{\int e^{-\beta \mathrm{\Phi }(r_1,...,r_N)\mathrm{d}{r}_1...\mathrm{d}{r}_N}}$

See also

• Compressibility equation
• Pressure equation
• Energy equation