On diffusion dynamics for continuous systems with singular superstable interaction

We consider the time evolution of states for continuous infinite particle systems which corresponds to nonequilibrium diffusion dynamics. For initial states mu(0) which are perturbations of the equilibrium we obtain a bound for finite volume nonequilibrium correlation functions and their continuity in time uniformly in volume for any finite time interval. This gives the possibility to construct the time evolution of correlation functions and corresponding states in the thermodynamic limit. (C) 2004 American Institute of Physics.