  We present a novel procedure for calculating non-equilibrium two-point
Green's functions in the $O(N) \phi^{4}$ theory at large $N$. The
non-equilibrium density matrix $\rho$ is constructed via the Jaynes-Gibbs
principle of maximal entropy and it is directly implemented into the
Dyson-Schwinger equations through initial value conditions. In the large $N$
limit we perform an explicit evaluation of two-point Green's functions for two
illustrative choices of $\rho$.
