For a system of classical particles interacting via stable pairwise integrable and positive many-body (nonpairwise) finite-range potentials, we prove the existence of a solution of the symmetrized Kirkwood-Salsburg equation.
Similar content being viewed by others
References
W. Greenberg, “Thermodynamic states of classical systems,” Comm. Math. Phys., 22, 259–268 (1971).
H. Moraal, “The Kirkwood-Salsburg equation and the virial expansion for many-body potentials,” Phys. Lett. A, 59, No. 1, 9–10 (1976).
D. Ruelle, Statistical Mechanics. Rigorous Results, Benjamin, New York (1969).
G. Gallavotti and E. Verboven, “On the classical KMS boundary conditions,” Nuovo Cimento B, 28, No. 1, 274–286 (1975).
N. N. Bogolyubov, D. Ya. Petrina, and B. I. Khatset, “Mathematical description of the equilibrium states of classical systems on the basis of the formalism of canonical ensemble,” Teor. Mat. Fiz., 1, No. 2, 251–274 (1969).
D. Ya. Petrina, V. I. Gerasimenko, and P. V. Malyshev, Mathematical Foundations of Classical Statistical Mechanics, Gordon & Breach, London (1989).
V. I. Skrypnyk, “On the Gibbs quantum and classical systems of particles with three-particle forces, ” Ukr. Mat. Zh., 58, No. 7, 976–996 (2006).
V. I. Skrypnyk, “Method of functional integral for Gibbs systems with many-particle potentials. I, ” Teor. Mat. Fiz., 88, No. 1, 115–121 (1991).
A. Rebenko, “Polymer expansions for continuous classical systems with many-body interaction,” Meth. Funct. Anal. Top., 11, No. 1, 73–87 (2005).
Author information
Authors and Affiliations
Additional information
Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 60, No. 8, pp. 1138–1143, August, 2008.
Rights and permissions
About this article
Cite this article
Skrypnyk, V.I. Solutions of the Kirkwood-Salsburg equation for particles with finite-range nonpairwise repulsion. Ukr Math J 60, 1329–1334 (2008). https://doi.org/10.1007/s11253-009-0122-3
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11253-009-0122-3