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TMF, 2018, Volume 194, Number 3, Pages 452–467 (Mi tmf9333)  

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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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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