Abstract
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 fluctuations, 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.
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Gruber, C., Lugrin, C. & Martin, P.A. Equilibrium properties of classical systems with long-range forces. BBGKY equation, neutrality, screening, and sum rules. J Stat Phys 22, 193–236 (1980). https://doi.org/10.1007/BF01008049
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DOI: https://doi.org/10.1007/BF01008049