Journal of Statistical Physics, Vol. 22, No. 2, 1980. p. 193-236.
We introduce a generalization of the BBGKY equation to define the equilibrium states for systems with long-range forces and study the properties of such states. We show that there are properties typical of short-range forces
(shape independence, normal fluctuations, asymptotic behavior of correlation functions) and others which are typical of long-range forces (possible shape dependence, neutrality, sum rules and screening, abnormal fluctua-
tions, boundedness of the internal electric field). If the force decreases at infinity faster than the Coulomb force, the properties will be those typical of short-range forces ; on the other hand, if the force decreases at infinity as the Coulomb force or slower, the properties will be those typical of long-range forces.