  We present the path-integral solutions to the distributions in classical
(Gibbs) and quantum (Wigner) statistical mechanics. The kernel of the
distributions are derived in two ways - one by time slicing and defining the
appropriate short-time interval phase space matrix element and second by making
use of the kernel in the path-integral approach to quantum mechanics. We show
that the two approaches are perturbatively identical. We also present another
computation for the Wigner kernel, which is also the Liouville kernel, for the
harmonic oscillator and free particle. These kernels may be used as the
starting point in the perturbative expansion of the Wigner kernel for any
potential. With the kernel solved, we essentially solve also the distributions
in classical and quantum statistical mechanics.
