Geodesic
Limit distribution functions in classical statistical physics
Teoretičeskaâ i matematičeskaâ fizika, Tome 21 (1974) no. 3, pp. 388-401 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The thermodynamic limit for the partial distribution functions is considered on the basis of Bogolyubov's generating functional method. For one-component systems of hard spheres with binary interaction whose potential at large distances decreases faster than $r_{12}^{-3}$, it is shown that the limit generating functional of the grand canonical ensemble, and when certain “stability conditions” are satisfied, of the canonical ensemble as well: 1) exists in the whole interval of states of the thermodynamic system; 2) defines limit distribution functions; 3) satisfies Bogolyubov's functional equation; 4) can be expanded in a convergent functional Taylor series. 
@article{TMF_1974_21_3_a9,
     author = {G. I. Nazin},
     title = {Limit distribution functions in classical statistical physics},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {388--401},
     year = {1974},
     volume = {21},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1974_21_3_a9/}
}
TY  - JOUR
AU  - G. I. Nazin
TI  - Limit distribution functions in classical statistical physics
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1974
SP  - 388
EP  - 401
VL  - 21
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_1974_21_3_a9/
LA  - ru
ID  - TMF_1974_21_3_a9
ER  - 
%0 Journal Article
%A G. I. Nazin
%T Limit distribution functions in classical statistical physics
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1974
%P 388-401
%V 21
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_1974_21_3_a9/
%G ru
%F TMF_1974_21_3_a9
G. I. Nazin. Limit distribution functions in classical statistical physics. Teoretičeskaâ i matematičeskaâ fizika, Tome 21 (1974) no. 3, pp. 388-401. http://geodesic.mathdoc.fr/item/TMF_1974_21_3_a9/

[1] G. Gallavotti, S. Miracle-Sole, Commun. Math. Phys., 5 (1967), 317 | DOI | MR | Zbl

[2] D. Ruelle, Ann. Phys., 25 (1963), 109 | DOI | MR

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

[4] R. L. Dobrushin, Teoriya veroyatnostei i ee primeneniya, 15 (1970), 469 | Zbl

[5] R. L. Dobrushin, Funktsionalnyi analiz i ego prilozheniya, 2 (1968), 31 | Zbl

[6] R. L. Dobrushin, Funktsionalnyi analiz i ego prilozheniya, 3 (1969), 27 | Zbl

[7] N. N. Bogolyubov, Problemy dinamicheskoi teorii v statisticheskoi fizike, GITTL, 1946 | MR

[8] D. Ryuel, Statisticheskaya mekhanika, «Mir», 1971

[9] P. Levi, Konkretnye problemy funktsionalnogo analiza, «Nauka», 1967 | MR

[10] A. N. Kolmogorov, S. V. Fomin, Elementy teorii funktsii i funktsionalnogo analiza, «Nauka», 1972 | MR

[11] A. Gurvits, R. Kurant, Teoriya funktsii, «Mir», 1968 | MR

[12] Funktsionalnyi analiz, «Nauka», 1972 | MR