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Teoreticheskaya i Matematicheskaya Fizika, 2018, Volume 194, Number 3, Pages 452–467
DOI: https://doi.org/10.4213/tmf9333 (Mi tmf9333) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Obtaining the thermodynamic relations for the Gibbs ensemble using the maximum entropy method

V. V. Ryazanov

Institute for Nuclear Research, National Academy of Sciences of Ukraine, Kiev, Ukraine
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DOI: https://doi.org/10.4213/tmf9333
Abstract: As a generating functional of the Gibbs ensemble, we use the Laplace transform of the complex (or generalized) Poisson measure. We use the maximum entropy principle to determine the form of the generating function of this distribution. We consider the cases where only the mathematical expectation is known and where the mathematical expectation and the second moment are known. In the latter case, the equation of state has a transcendental form. In the both cases, if there is no interaction, then the obtained relations lead to expressions for an ideal gas.
Keywords: Gibbs system, grand canonical ensemble, generalized Poisson distribution, maximum entropy principle.
Received: 10.01.2017
Revised: 22.03.2017
English version:
Theoretical and Mathematical Physics, 2018, Volume 194, Issue 3, Pages 390–403
DOI: https://doi.org/10.1134/S0040577918030078
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. V. Ryazanov, “Obtaining the thermodynamic relations for the Gibbs ensemble using the maximum entropy method”, TMF, 194:3 (2018), 452–467; Theoret. and Math. Phys., 194:3 (2018), 390–403
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf/v194/i3/p452
    • This publication is cited in the following 1 articles:
    1. M. Bounkhel, L. Tadj, R. Hedjar, “Entropy maximization for the busy period of a single server queue”, Communications in Statistics - Theory and Methods, 52:23 (2023), 8555  crossref  mathscinet
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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