Variational principle for the equilibrium wigner distribution function

A variational principle is derived for the equilibrium Wigner distribution function of quantum statistical mechanics. This provides an alternative to the usual Wigner-Kirkwood expansion method of calculating quantum corrections to the structural and thermodynamic properties of systems. As an illustration, the method is applied to the second virial coefficient of a Lennard-Jones gas, and it is found that the simplest trial function gives results superior to the Wigner-Kirkwood series.