  The nonequilibrium dynamics of quantum fields is an initial-value problem,
which can be described by Kadanoff-Baym equations. Typically, and in particular
when numerical solutions are demanded, these Kadanoff-Baym equations are
restricted to Gaussian initial states. However, physical initial states are
non-Gaussian correlated initial states. In particular, renormalizability
requires the initial state to feature n-point correlations that asymptotically
agree with the vacuum correlations at short distances. In order to identify
physical nonequilibrium initial states, it is therefore a precondition to
describe the vacuum correlations of the interacting theory within the
nonequilibrium framework. In this paper, Kadanoff-Baym equations for
non-Gaussian correlated initial states describing vacuum and thermal
equilibrium are derived from the 2PI effective action. A diagrammatic method
for the explicit construction of vacuum and thermal initial correlations from
the 2PI effective action is provided. We present numerical solutions of
Kadanoff-Baym equations for a real scalar Phi^4 quantum field theory which take
the thermal initial 4-point correlation as the leading non-Gaussian correction
into account. We find that this minimal non-Gaussian initial condition yields
an approximation to the complete equilibrium initial state that is
quantitatively and qualitatively significantly improved as compared to Gaussian
initial states.
