2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/55659We present a novel procedure for calculating non-equilibrium two-point Green's functions in the $O(N) ϕ^{4}$ theory at large $N$. The non-equilibrium density matrix $ρ$ 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 $ρ$.4 pages, REVTeX, no figures, references added, minor corrections in textHigh Energy Physics - TheoryHigh Energy Physics - Phenomenologytext