Maslov's complex germ and the asymptotic formula for the Gibbs canonical distribution

O. Yu. Shvedov

Matematičeskie zametki, Tome 64 (1998) no. 4, pp. 622-636

Résumé

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.