  We reformulate time evolution of systems in mixed states in terms of the
classical observables of correlators using the Weyl correspondence rule. The
resulting equation of motion for the Wigner functional of the density matrix is
found to be of the Liouville type. To illustrate the methods developed, we
explicitly consider a scalar theory with quartic self-interaction and derive
the short time behaviour with the non-interacting thermal density matrix as
initial condition. In the scalar case, the complete correlator hierarchy is
studied and restrictions are derived for spatially homogeneous initial
conditions and systems with unbroken symmetry.
