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 TMF, 1986, Volume 66, Number 3, Pages 463–480 (Mi tmf4642)

Bogolyubov generating functional method in statistical mechanics and the analog of the transformation to collective variables

N. N. Bogolyubov (Jr.), A. K. Prikarpatskii

Abstract: ]3ogolyubov's functional equations for the distribution functions in statistical mechanics for equilibrium and nonequilibrium many-particle systems are studied. An analog of the transformation to "collective" variables on the basis of an exact solution of ]3ogolyubov's functional equation in the equilibrium case is proposed. ]3ogolyubov's method is used to obtain a functional equation of Kirkwood-Salsburg-Symanzik type. A path integral method is developed for constructing the generating functionals of the distribution functions.

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English version:
Theoretical and Mathematical Physics, 1986, 66:3, 305–317

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Citation: N. N. Bogolyubov (Jr.), A. K. Prikarpatskii, “Bogolyubov generating functional method in statistical mechanics and the analog of the transformation to collective variables”, TMF, 66:3 (1986), 463–480; Theoret. and Math. Phys., 66:3 (1986), 305–317

Citation in format AMSBIB
\Bibitem{BogPri86} \by N.~N.~Bogolyubov (Jr.), A.~K.~Prikarpatskii \paper Bogolyubov generating functional method in statistical mechanics and the analog of the transformation to collective variables \jour TMF \yr 1986 \vol 66 \issue 3 \pages 463--480 \mathnet{http://mi.mathnet.ru/tmf4642} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=847438} \transl \jour Theoret. and Math. Phys. \yr 1986 \vol 66 \issue 3 \pages 305--317 \crossref{https://doi.org/10.1007/BF01018230} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1986E586400013} 

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This publication is cited in the following articles:
1. V. V. Ryazanov, “Obtaining the thermodynamic relations for the Gibbs ensemble using the maximum entropy method”, Theoret. and Math. Phys., 194:3 (2018), 390–403
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