Nonequilibrium dynamics of infinite particle systems with infinite range interactions

We discuss the existence and uniqueness of nonequilibrium dynamics of infinitely many particles interacting via superstable pair interactions in one and two dimensions. The interaction is allowed to be of infinite range and singular at the origin. Under suitable regularity conditions on the interaction potential, we show that if the potential decreases polynomially as the distance between interacting two particles increases, then the tempered solution to the system of Hamiltonian equations exists. Moreover, if the potential satisfies further that either it has a subexponential decreasing rate or it is everywhere two-times continuously differentiable, then we show that the tempered solution is unique. The results extend those of Dobrushin and Fritz obtained for finite range interactions.(C) 1999 American Institute of Physics. [S0022-2488(99)01609-6].