Geodesic
Generalization of the Bogoliubov–Zubarev theorem for dynamic
Teoretičeskaâ i matematičeskaâ fizika, Tome 194 (2018) no. 1, pp. 137-150 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We present the motivation, formulation, and modified proof of the Bogoliubov–Zubarev theorem connecting the pressure of a dynamical object with its energy within the framework of a classical description and obtain a generalization of this theorem to the case of dynamical compressibility. In both cases, we introduce the volume of the object into consideration using a singular addition to the Hamiltonian function of the physical object, which allows using the concept of the Bogoliubov quasiaverage explicitly already on a dynamical level of description. We also discuss the relation to the same result known as the Hellmann–Feynman theorem in the framework of the quantum description of a physical object.
Keywords: pressure, compressibility, Hamiltonian function, quasiaverage, homogeneous potential.
Mots-clés : canonical scale transformation 
@article{TMF_2018_194_1_a6,
     author = {Yu. G. Rudoi},
     title = {Generalization of {the~Bogoliubov{\textendash}Zubarev} theorem for dynamic},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {137--150},
     year = {2018},
     volume = {194},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2018_194_1_a6/}
}
TY  - JOUR
AU  - Yu. G. Rudoi
TI  - Generalization of the Bogoliubov–Zubarev theorem for dynamic
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2018
SP  - 137
EP  - 150
VL  - 194
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_2018_194_1_a6/
LA  - ru
ID  - TMF_2018_194_1_a6
ER  - 
%0 Journal Article
%A Yu. G. Rudoi
%T Generalization of the Bogoliubov–Zubarev theorem for dynamic
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2018
%P 137-150
%V 194
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_2018_194_1_a6/
%G ru
%F TMF_2018_194_1_a6
Yu. G. Rudoi. Generalization of the Bogoliubov–Zubarev theorem for dynamic. Teoretičeskaâ i matematičeskaâ fizika, Tome 194 (2018) no. 1, pp. 137-150. http://geodesic.mathdoc.fr/item/TMF_2018_194_1_a6/

[1] G. Gelman, Kvantovaya khimiya, BINOM. Laboratoriya znanii, M., 2012

[2] R. P. Feynman, “Forces in Molecules”, Phys. Rev., 56:4 (1939), 340–347 | DOI

[3] S. Balasubramanian, “A note on the generalized Hellmann–Feynman theorem”, Am. J. Phys., 58:12 (1990), 1204–1205 | DOI

[4] R. Feinman, Statisticheskaya mekhanika, Mir, M., 1975 | Zbl

[5] F. Reif, Statisticheskaya fizika, Berkleevskii kurs fiziki, 5, Nauka, M., 1977

[6] N. N. Bogolyubov, Problemy dinamicheskoi teorii v statisticheskoi fizike, Gostekhizdat, M.–L., 1946 | MR

[7] N. N. Bogolyubov, Sobranie nauchnykh trudov v 12 tomakh. Statisticheskaya mekhanika, v. 5, Neravnovesnaya statisticheskaya mekhanika. 1939–1980, Nauka, M., 2006

[8] D. N. Zubarev, Neravnovesnaya statisticheskaya termodinamika, Nauka, M., 1971 | MR

[9] D. N. Zubarev, V. G. Morozov, G. Repke, Statisticheskaya mekhanika neravnovesnykh protsessov, v. 1, Fizmatlit, M., 2002 | MR | Zbl

[10] N. N. Bogolyubov, Kvazisrednie v zadachakh statisticheskoi mekhaniki, Preprint D-781, OIYaI, Dubna, 1961

[11] Yu. G. Rudoi, A. D. Sukhanov, “Termodinamicheskie fluktuatsii v podkhodakh Gibbsa i Einshteina”, UFN, 170:12 (2000), 1265–1296 | DOI

[12] I. A. Kvasnikov, Termodinamika i statisticheskaya fizika, v. 1, Teoriya ravnovesnykh sistem: termodinamika, Izd-vo MGU, M., 1991 | MR

[13] V. S. Vladimirov, Obobschennye funktsii v matematicheskoi fizike, Nauka, M., 1976 | MR

[14] Ya. P. Terletskii, Statisticheskaya fizika, Vysshaya shkola, M., 1994 | MR

[15] Yu. G. Rudoy, “The Bogolyubov method of quasiaverages solves the problem of pressure fluctuations in the Gibbs statistical mechanics”, Cond. Mat. Phys., 12:4 (2009), 581–592 | DOI