Geodesic
Relationships between the correlation functions in classical statistical physics
Teoretičeskaâ i matematičeskaâ fizika, Tome 3 (1970) no. 1, pp. 115-125 
F. A. Berezin. Relationships between the correlation functions in classical statistical physics. Teoretičeskaâ i matematičeskaâ fizika, Tome 3 (1970) no. 1, pp. 115-125. http://geodesic.mathdoc.fr/item/TMF_1970_3_1_a9/
@article{TMF_1970_3_1_a9,
     author = {F. A. Berezin},
     title = {Relationships between the correlation functions in classical statistical physics},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {115--125},
     year = {1970},
     volume = {3},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1970_3_1_a9/}
}
TY  - JOUR
AU  - F. A. Berezin
TI  - Relationships between the correlation functions in classical statistical physics
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1970
SP  - 115
EP  - 125
VL  - 3
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_1970_3_1_a9/
LA  - ru
ID  - TMF_1970_3_1_a9
ER  - 
%0 Journal Article
%A F. A. Berezin
%T Relationships between the correlation functions in classical statistical physics
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1970
%P 115-125
%V 3
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_1970_3_1_a9/
%G ru
%F TMF_1970_3_1_a9

Voir la notice de l'article provenant de la source Math-Net.Ru

The aim of the paper is to establish an explicit expression for the higher correlation ftmction in the grand canonical ensemble in terms of file first and second correlation functions. The relationship Obtained has the nature of an expansion in powers of the first correlation function (the density), the first term of the expansion coinciding with the so-called superposition approximation introduced by Kirkwood [1]: $\displaystyle r_n(x_1,\dots, x_n)=\prod_{i, where $r_k(x_1,\dots, x_k)=\rho_1^{-1}(x_1)\dots \rho_1^{-1}(x_k)\rho_k(x_1,\dots, x_k)$ is the normalized correlation function. The convergence of the series obtained is not investigated.

[1] I. G. Kirkwood, J. Chem. Phys., 3 (1935), 300 | DOI | Zbl

[2] N. N. Bogolyubov, B. I. Khatset, DAN SSSR, 66 (1949), 321 | MR | Zbl

[3] B. I. Khatset, Nauch. zap. Zhitomirskogo ped. instituta, fiz.-mat. seriya, III (1956), 139

[4] D. Ruelle, Helv. Phys. Acta, 36 (1963), 183 | MR | Zbl

[5] T. Khill, Statisticheskaya mekhanika, IL, 1960

[6] N. N. Bogolyubov, D. Ya. Petrina, B. I. Khatset, TMF, 1 (1969), 251