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Teoreticheskaya i Matematicheskaya Fizika, 2008, Volume 155, Number 2, Pages 312–316
DOI: https://doi.org/10.4213/tmf6213 (Mi tmf6213) 		 
This article is cited in 12 scientific papers (total in 12 papers)

Gibbs and Bose–Einstein distributions for an ensemble of self-adjoint operators in classical mechanics

V. P. Maslov

M. V. Lomonosov Moscow State University
Full-text PDF (395 kB) Citations (12)
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DOI: https://doi.org/10.4213/tmf6213
Abstract: We introduce the notion of an ensemble of self-adjoint operators and formulate theorems relating the occupation numbers to the number of eigenvalues of the ensemble. We formulate a theorem for the Gibbs distribution in classical mechanics.
Keywords: Gibbs distribution, Bose–Einstein distribution, Bose condensate, ordered sampling with returns, disordered sampling with returns, Gibbs ensemble.
Received: 22.02.2008
English version:
Theoretical and Mathematical Physics, 2008, Volume 155, Issue 2, Pages 775–779
DOI: https://doi.org/10.1007/s11232-008-0066-z
Bibliographic databases:
Language: Russian
Citation: V. P. Maslov, “Gibbs and Bose–Einstein distributions for an ensemble of self-adjoint operators in classical mechanics”, TMF, 155:2 (2008), 312–316; Theoret. and Math. Phys., 155:2 (2008), 775–779
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/tmf6213
  • https://doi.org/10.4213/tmf6213
  • https://www.mathnet.ru/eng/tmf/v155/i2/p312
    • This publication is cited in the following 12 articles:
    1. V. P. Maslov, “Probability Distribution for a Hard Liquid”, Math. Notes, 97:6 (2015), 909–918  mathnet  mathnet  crossref  isi  scopus
    2. V. P. Maslov, “On the Semiclassical Transition in the Quantum Gibbs Distribution”, Math. Notes, 97:4 (2015), 565–574  mathnet  mathnet  crossref  isi  scopus
    3. V. P. Maslov, “Van der Waals equation from the viewpoint of probability distribution and the triple point as the critical point of the liquid-to-solid transition”, Russ. J. Math. Phys., 22:2 (2015), 188  crossref
    4. V. P. Maslov, “Distribution corresponding to classical thermodynamics”, Phys. Wave Phen., 23:2 (2015), 81  crossref
    5. V. P. Maslov, “A mathematical theory of the supercritical state serving as an effective means of destruction of chemical warfare agents”, Math Notes, 94:3-4 (2013), 532  crossref
    6. Maslov V.P., “Solution of the Gibbs paradox using the notion of entropy as a function of the fractal dimension”, Russ. J. Math. Phys., 17:3 (2010), 288–306  crossref  mathscinet  zmath  isi  elib  scopus
    7. Maslov V.P., “New global distributions in number theory and their applications”, J. Fixed Point Theory Appl., 8:1 (2010), 81–111  crossref  mathscinet  zmath  isi  scopus
    8. Maslov V.P., “Threshold levels in economics and time series”, Math. Notes, 85:3-4 (2009), 305–321  crossref  zmath  isi  elib  scopus
    9. V. P. Maslov, “Mathematical economics and thermodynamics: Crises as phase transitions”, Math Notes, 86:5-6 (2009), 879  crossref
    10. V. P. Maslov, “Refinement of a criterion for superfluidity of a classical liquid in a nanotube”, Theoret. and Math. Phys., 155:3 (2008), 959–963  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    11. V. P. Maslov, “New distribution formulas for classical gas, clusters, and phase transitions”, Theoret. and Math. Phys., 157:2 (2008), 1577–1594  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    12. Maslov V.P., “On the superfluidity of classical liquid in nanotubes. IV”, Russ. J. Math. Phys., 15:2 (2008), 280–290  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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