We present a particular approach to the non-equilibrium dynamics of quantum field theory. This approach is based on the Jaynes-Gibbs principle of the maximal entropy and its implementation, throughout the initial-value data, into the dynamical equations for Green’s functions. We use the&fgr;4theory in the largeNlimit to show how our method works by calculating the pressure for a system which is invariant under both spatial and temporal translations. ©1999 American Institute of Physics.