Approximation Methods in Classical Statistical Mechanics

The pair distribution function for a classical fluid in thermal equilibrium is found to be more closely approximated by the Percus and Yevick (Phys. Rev., 110: 1(1958)) approximation than by the Bogoliubov-Born-Green- Kirkwood-Yvon (B.B.G.K.Y.) approximation or the hypernettedchain approximation. It is noted that the reason for this finding lies in the fact that the Percus and Yevick approximation chooses a quite advantageous function for making a Taylor expansion of the appropriate equation for a grand canonical ensemble. (T.F.H.)