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

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/N2), etc. The asymptotics of free energy and of the partition function asN→∞ is found. An asymptotic formula approximating the normalized canonical distribution in theL1 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.