Abstract
The Gibbs canonical distribution for a system of N classical particles is studied under the following conditions: the external potential isO(1), the potential of pairwise interaction isO(1/N), the potential of triple interaction isO(1/N 2), etc. The asymptotics of free energy and of the partition function asN→∞ is found. An asymptotic formula approximating the normalized canonical distribution in theL 1 norm asN→∞ is also constructed. It is proved that the chaos property is satisfied fork-particle distributions,k = const, and is not satisfied for theN-particle distribution.
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Translated fromMatematicheskie Zametki, Vol. 64, No. 4, pp. 622–636, October, 1998.
The author wishes to thank Professor V. P. Maslov, member of the Russian Academy of Sciences, for setting the problem, permanent attention to the work, useful discussion on a number if issues, and valuable remarks.
This research was supported by the Royal Society of Great Britain.
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Shvedov, O.Y. Maslov's complex germ and the asymptotic formula for the Gibbs canonical distribution. Math Notes 64, 537–550 (1998). https://doi.org/10.1007/BF02314637
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DOI: https://doi.org/10.1007/BF02314637