Equilibrium time evolutions and BBGKY hierarchy equations of large classical systems

Summary We show the existence of a time evolution {P _t ; t of a locally perturbed equilibrium state P of infinitely many particles in {suv}, v1, evolving under the action of the infinite Newtonian dynamics associated to the same smooth, finite range pair potential as the equilibrium state itself. Moreover, it is shown that {P _t ; t solves the weak BBGKY hierarchy equations. The treatment of this problem will be done in the general setting of so called ( ) point processes developed in 11, 10] and 4] and will require the method of moments.