Geodesic
Quantization of Boltzmann Entropy: Pairs and Correlation Function
Teoretičeskaâ i matematičeskaâ fizika, Tome 131 (2002) no. 2, pp. 261-277 
V. P. Maslov. Quantization of Boltzmann Entropy: Pairs and Correlation Function. Teoretičeskaâ i matematičeskaâ fizika, Tome 131 (2002) no. 2, pp. 261-277. http://geodesic.mathdoc.fr/item/TMF_2002_131_2_a7/
@article{TMF_2002_131_2_a7,
     author = {V. P. Maslov},
     title = {Quantization of {Boltzmann} {Entropy:} {Pairs} and {Correlation} {Function}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {261--277},
     year = {2002},
     volume = {131},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2002_131_2_a7/}
}
TY  - JOUR
AU  - V. P. Maslov
TI  - Quantization of Boltzmann Entropy: Pairs and Correlation Function
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2002
SP  - 261
EP  - 277
VL  - 131
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_2002_131_2_a7/
LA  - ru
ID  - TMF_2002_131_2_a7
ER  - 
%0 Journal Article
%A V. P. Maslov
%T Quantization of Boltzmann Entropy: Pairs and Correlation Function
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2002
%P 261-277
%V 131
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_2002_131_2_a7/
%G ru
%F TMF_2002_131_2_a7

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

We consider the Gibbs statistical ensemble. We introduce the statistical-weight operator $\widehat\Gamma$, construct the entropy operator $\widehat S$ of the ensemble using the Boltzmann formula $\widehat S=\ln\widehat\Gamma$ and define the free-energy operator. We find asymptotic expressions for free-energy eigenvalues with pair correlations taken into account in the limit as the number of systems in the ensemble tends to infinity.

[1] V. P. Maslov, Funkts. analiz i ego prilozh., 34:4 (2000), 35–48 | DOI | MR | Zbl

[2] V. P. Maslov, TMF, 125:2 (2000), 297–314 | DOI | MR

[3] V. P. Maslov, TMF, 129:3 (2001), 464–490 | DOI | MR | Zbl

[4] V. P. Maslov, Kvantovanie termodinamiki i ultravtorichnoe kvantovanie, NITs “Regulyarnaya i Khaoticheskaya Dinamika”; URSS, Izhevsk, 2001

[5] L. D. Landau, E. M. Lifshits, Statisticheskaya fizika, Nauka, M., 1976 | MR

[6] E. S. Venttsel, Teoriya veroyatnostei, Fizmatgiz, M., 1962 | MR

[7] E. M. Lifshits, L. P. Pitaevskii, Statisticheskaya fizika, Nauka, M., 1979 | Zbl

[8] V. P. Maslov, Kompleksnyi metod VKB v nelineinykh uravneniyakh, Nauka, M., 1977 | MR

[9] V. P. Maslov, Teoriya vozmuschenii i asimptoticheskie metody, Nauka, M., 1978 | MR

[10] F. A. Berezin, Metod vtorichnogo kvantovaniya, Nauka, M., 1987 | MR

[11] V. P. Maslov, O. Yu. Shvedov, Metod kompleksnogo rostka v mnogochastichnykh zadachakh i zadachakh kvantovoi teorii polya, URSS, M., 2000