Geodesic
Maslov's complex germ and the asymptotic formula for the Gibbs canonical distribution
Matematičeskie zametki, Tome 64 (1998) no. 4, pp. 622-636 
O. Yu. Shvedov. Maslov's complex germ and the asymptotic formula for the Gibbs canonical distribution. Matematičeskie zametki, Tome 64 (1998) no. 4, pp. 622-636. http://geodesic.mathdoc.fr/item/MZM_1998_64_4_a15/
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     author = {O. Yu. Shvedov},
     title = {Maslov's complex germ and the asymptotic formula for the {Gibbs} canonical distribution},
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     year = {1998},
     volume = {64},
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     url = {http://geodesic.mathdoc.fr/item/MZM_1998_64_4_a15/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The Gibbs canonical distribution for a system of $N$ classical particles is studied under the following conditions: the external potential is $O(1)$, the potential of pairwise interaction is $O(1/N)$, the potential of triple interaction is $O(1/N^2)$, etc. The asymptotics of free energy and of the partition function as $N\to\infty$ is found. An asymptotic formula approximating the normalized canonical distribution in the $L_1$ norm as $N\to\infty$ is also constructed. It is proved that the chaos property is satisfied for $k$-particle distributions,$k=\mathrm{const}$, and is not satisfied for the $N$-particle distribution.

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