The Jaynes-Gibbs principle of maximal entropy and the non-equilibrium propagators of the O(N) phi^4 theory at large N

Abstract

We 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 $ρ$.