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Geometric “quantization” of thermodynamics and statistical corrections at critical points
Teoretičeskaâ i matematičeskaâ fizika, Tome 101 (1994) no. 3, pp. 433-441 Cet article a éte moissonné depuis la source Math-Net.Ru

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Gibbs thermodynamics is treated as a two-dimensional manifold, called Lagrangian by the author, in a 4-dimensional phase space in which the temperature and pressure play the role of coordinates and the entropy and volume the role of momenta. The tunneling canonical operator determines the asymptotic behavior of the partition function. This treatment is generalized to the case of thermodynamics with intensive and extensive coordinates. A new axiomatics of thermodynamics and quasithermodynamics is given. 
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     title = {Geometric {\textquotedblleft}quantization{\textquotedblright} of thermodynamics and statistical corrections at critical points},
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V. P. Maslov. Geometric “quantization” of thermodynamics and statistical corrections at critical points. Teoretičeskaâ i matematičeskaâ fizika, Tome 101 (1994) no. 3, pp. 433-441. http://geodesic.mathdoc.fr/item/TMF_1994_101_3_a10/

[1] Arnold V. I., Matematicheskie metody klassicheskoi mekhaniki, Nauka, M., 1974 | MR

[2] Maslov V. P., Chebotarev A. M., “O vtorom chlene logarifmicheskoi asimptotiki funktsionalnykh integralov”, Itogi nauki i tekhniki, 19, 1982, 127–154 | MR | Zbl

[3] Giiemin V., Sternberg S., Geometricheskie asimptotiki, Mir, M., 1981 | MR

[4] Czyz J., Repts Math. Phys., 15:1 (1979), 57–97 | DOI | MR | Zbl

[5] Weinstein A., Lect. Notes Math., 459, 1975, 341–372 | DOI | MR | Zbl

[6] Lion Zh., Vern M., Predstavlenie Veilya, indeks Maslova i teta-ryady, Mir, M., 1983 | MR

[7] Yoshikava B., Hokkaido Math. J., 4 (1975), 8–38 | DOI | MR

[8] Maslov V. P., Asimptoticheskie metody i teoriya vozmuschenii, Nauka, M., 1988 | MR

[9] Maslov V. P., UMN, 38:6 (1983), 3–36 | MR | Zbl

[10] Arnold V. I., Varchenko A. N., Gusein-Zade S. M., Osobennosti differentsiruemykh otobrazhenii, t. I, Nauka, M., 1982 ; т. II, 1984 | MR

[11] Maslov V. P., “Analiticheskoe prodolzhenie asimptoticheskikh formul i aksiomatika termodinamiki i kvazitermodinamiki”, Funktsionalnyi analiz, 28:4 (1994), 28–41 | MR

[12] Landau L. D., Lifshits E. M., Statisticheskaya fizika, Nauka, M., 1964 | Zbl