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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
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.
DOI:
https://doi.org/10.4213/tmf9333
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English version:
Theoretical and Mathematical Physics, 2018, 194:3, 390–403
Bibliographic databases:
Received: 10.01.2017 Revised: 22.03.2017
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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\pages 390--403
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http://mi.mathnet.ru/eng/tmf9333https://doi.org/10.4213/tmf9333 http://mi.mathnet.ru/eng/tmf/v194/i3/p452
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