Geodesic
Generating functional method and virial expansions in nonequilibrium statistical mechanics
Teoretičeskaâ i matematičeskaâ fizika, Tome 3 (1970) no. 2, pp. 287-300 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The concept is introduced of a generating functional. This enables one to find all the many-particle distribution functions by differentiation with respect to the functional argument. An equation is found for this functional which is equivalent to the equation for the density matrix of the system. It is shown that the steady-state solution of this equation, complemented by the principle of spatial correlation relaxation (the latter can be formulated simply in terms of the generating functional), is equivalent to the Gibbs distribution. An integral equation is found for the generating functional at the stage of evolution when the state of the system is described by a distribution function and a method of solving this equation as a series in powers of the density is developed. 
@article{TMF_1970_3_2_a13,
     author = {S. V. Peletminskii and A. A. Yatsenko},
     title = {Generating functional method and virial expansions in nonequilibrium statistical mechanics},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {287--300},
     year = {1970},
     volume = {3},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1970_3_2_a13/}
}
TY  - JOUR
AU  - S. V. Peletminskii
AU  - A. A. Yatsenko
TI  - Generating functional method and virial expansions in nonequilibrium statistical mechanics
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1970
SP  - 287
EP  - 300
VL  - 3
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_1970_3_2_a13/
LA  - ru
ID  - TMF_1970_3_2_a13
ER  - 
%0 Journal Article
%A S. V. Peletminskii
%A A. A. Yatsenko
%T Generating functional method and virial expansions in nonequilibrium statistical mechanics
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1970
%P 287-300
%V 3
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_1970_3_2_a13/
%G ru
%F TMF_1970_3_2_a13
S. V. Peletminskii; A. A. Yatsenko. Generating functional method and virial expansions in nonequilibrium statistical mechanics. Teoretičeskaâ i matematičeskaâ fizika, Tome 3 (1970) no. 2, pp. 287-300. http://geodesic.mathdoc.fr/item/TMF_1970_3_2_a13/

[1] N. N. Bogolyubov, Problemy dinamicheskoi teorii v statisticheskoi fizike, Gostekhizdat, 1946 | MR

[2] S. V. Peletminskii, A. A. Yatsenko, Preprint ITF-65-5, Kiev, 1968

[3] S. V. Peletminskii, A. A. Yatsenko, ZhETF, 53 (1967), 1327