Some remarks on nonequilibrium dynamics of infinite particle systems

Classical mechanics of infinitely many particles in dimensions one and two is considered, particles interacting by a superstable pair potential of finite range. The group of motion generated by Newton's equations is constructed in the space of locally finite configurations with a logarithmic order of energy fluctuations at infinity. A core of the Liouville operator is also described. Results of Dobrushin and the author and of Marchioro-Pellegrinotti-Pulvirenti are improved.