V. P. Maslov, V. E. Nazaikinskii, “Tunnel Canonical Operator in Thermodynamics”, Funktsional. Anal. i Prilozhen., 40:3 (2006), 12–29; Funct. Anal. Appl., 40:3 (2006), 173

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Funktsional'nyi Analiz i ego Prilozheniya, 2006, Volume 40, Issue 3, Pages 12–29
DOI: https://doi.org/10.4213/faa740 (Mi faa740)

This article is cited in 15 scientific papers (total in 15 papers)

Tunnel Canonical Operator in Thermodynamics

V. P. Maslov^ab, V. E. Nazaikinskii^b

^a M. V. Lomonosov Moscow State University, Faculty of Physics
^b A. Ishlinsky Institite for Problems in Mechanics, Russian Academy of Sciences

Full-text PDF (265 kB) Citations (15)

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DOI: https://doi.org/10.4213/faa740

Abstract: We construct a natural measure on the thermodynamic Lagrangian manifold. The measure is defined via the kinetic coefficients. We study the accuracy of the asymptotics provided by the canonical operator for the derivatives of the logarithm of the partition function.

Keywords: thermodynamic Lagrangian manifold, kinetic coefficients, measure, phenomenological semiclassical approximation, tunnel canonical operator, statistical potential.

Received: 29.03.2006

English version:
Functional Analysis and Its Applications, 2006, Volume 40, Issue 3, Pages 173–187
DOI: https://doi.org/10.1007/s10688-006-0029-9

Bibliographic databases:

Document Type: Article

UDC: 517.9+536.7

Language: Russian

Citation: V. P. Maslov, V. E. Nazaikinskii, “Tunnel Canonical Operator in Thermodynamics”, Funktsional. Anal. i Prilozhen., 40:3 (2006), 12–29; Funct. Anal. Appl., 40:3 (2006), 173–187

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/faa740

https://doi.org/10.4213/faa740

https://www.mathnet.ru/eng/faa/v40/i3/p12

This publication is cited in the following 15 articles:

V. G. Danilov, “Asymptotics of Fundamental Solutions of Parabolic Problems”, Math. Notes, 115:2 (2024), 182–191
Vladimir G. Danilov, Mark A. Rakhel, “Justification of the exact asymptotics of the fundamental solution for a degenerate parabolic equation with a small parameter”, Z Angew Math Mech, 104:3 (2024)
Evgeny A. Palkin, Anna A. Petrovich, 2022 IEEE 8th All-Russian Microwave Conference (RMC), 2022, 301
Danilov V.G., Rakhel M.A., “Development of Maslov'S Approach to the Construction of Nonoscillating Wkb-Type Solutions”, Russ. J. Math. Phys., 28:2 (2021), 179–187
Danilov V.G., “Forward and backward in time Cauchy problems for systems of parabolic-type PDE with a small parameter”, Math. Nachr., 289:7 (2016)
Danilov V.G., “Nonsmooth nonoscillating WKB–Maslov-type asymptotics for linear parabolic PDE”, Russ. J. Math. Phys., 23:2 (2016), 185–199
Ruuge A.E., “Fluctuations of Intensive Quantities in Statistical Thermodynamics”, Entropy, 15:11 (2013), 4889–4908
Danilov V.G., “Global-in-Time Asymptotic Solutions to Kolmogorov-Feller-Type Parabolic Pseudodifferential Equations with Small Parameter-Forward- and Backward-in-Time Motion”, Abstract Appl. Anal., 2013, 941878
Ruuge A.E., “A Tropical Analogue of the Pauli Problem and a Splitting of Quasithermodynamics”, Dokl. Math., 88:1 (2013), 482–485
Ruuge A.E., “An Asymptotics of the Pauli Problem in Thermodynamics”, Dokl. Math., 87:3 (2013), 360–363
Albeverio S., Danilov V., “Construction of global-in-time solutions to Kolmogorov-Feller pseudodifferential equations with a small parameter using characteristics”, Math. Nachr., 285:4 (2012), 426–439
Albeverio S., Danilov V.G., “Global in time solutions to Kolmogorov-Feller pseudodifferential equations with small parameter”, Russ. J. Math. Phys., 18:1 (2011), 10–25
Ruuge A.E., van Oystaeyen F., “ $q$ -Legendre transformation: partition functions and quantization of the Boltzmann constant”, J. Phys. A, 43:34 (2010), 345203, 30 pp.
Maslov V.P., “Revision of probability theory from the point of view of quantum statistics”, Russ. J. Math. Phys., 14:1 (2007), 66–95
V. P. Maslov, “The Lack-of-Preference Law and the Corresponding Distributions in Frequency Probability Theory”, Math. Notes, 80:2 (2006), 214–223

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Functional Analysis and Its Applications

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