We analyze some properties shown by extremal KMS states for interacting massive scalar fields propagating over Minkowski spacetime. These states have been recently constructed in the framework of perturbative algebraic quantum field theories by Fredenhagen and Lindner. In particular, we discuss the validity of the return to equilibrium property when the interaction Lagrangian has compact spatial support. If the adiabatic limit is considered, the return to equilibrium is in general not valid. This implies that an equilibrium state under the adiabatic limit for a perturbative interacting theory evolved with the free dynamics does not converge to the free equilibrium state. Actually, we show that the ergodic mean of this state converges to a non-equilibrium steady state (NESS) for the free theory. We thus compute the relative entropy among equilibrium states for different evolutions showing that such an extent is compatible with perturbation theory. We then analyze the entropy production in the NESS discussed above to estimate how far from equilibrium is this state.