N. N. Bogolyubov, D. Ya. Petrina, B. I. Khatset, “Mathematical description of the equilibrium state of classical systems on the basis of the canonical ensemble formalism”, TMF, 1:2 (1969), 251–274; Theoret. and Math. Phys., 1:2 (1969), 194

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Teoreticheskaya i Matematicheskaya Fizika, 1969, Volume 1, Number 2, Pages 251–274 (Mi tmf4568)

This article is cited in 54 scientific papers (total in 54 papers)

Mathematical description of the equilibrium state of classical systems on the basis of the canonical ensemble formalism

N. N. Bogolyubov, D. Ya. Petrina, B. I. Khatset

Full-text PDF (1951 kB) Citations (54)

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Abstract: This paper gives a rigorous mathematical description of the equilibrium state of the infinite system of particles on the basis of canonical ensemble theory. A proof is given of the existence and uniqueness of the limiting distribution functions and their analytical dependence on density. Results have been obtained by using methods developed by two of the authors in 1949, and based on the application of the theory of Banaeh spaces to the study of the equation forthe distribution functions.

Received: 26.03.1969

English version:
Theoretical and Mathematical Physics, 1969, Volume 1, Issue 2, Pages 194–212
DOI: https://doi.org/10.1007/BF01028046

Bibliographic databases:

Language: Russian

Citation: N. N. Bogolyubov, D. Ya. Petrina, B. I. Khatset, “Mathematical description of the equilibrium state of classical systems on the basis of the canonical ensemble formalism”, TMF, 1:2 (1969), 251–274; Theoret. and Math. Phys., 1:2 (1969), 194–212

Citation in format AMSBIB

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\by N.~N.~Bogolyubov, D.~Ya.~Petrina, B.~I.~Khatset

\paper Mathematical description of the equilibrium state of classical systems on the basis of the canonical ensemble formalism

\jour TMF

\yr 1969

\vol 1

\issue 2

\pages 251--274

\mathnet{http://mi.mathnet.ru/tmf4568}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=459460}

\transl

\jour Theoret. and Math. Phys.

\yr 1969

\vol 1

\issue 2

\pages 194--212

\crossref{https://doi.org/10.1007/BF01028046}

Linking options:

https://www.mathnet.ru/eng/tmf4568

https://www.mathnet.ru/eng/tmf/v1/i2/p251

Remarks

Comments on the paper “Mathematical description of the equilibrium state of classical systems on the basis of the canonical ensemble formalism” by N. N. Bogolyubov, D. Ya. Petrina, and B. I. Khatset
I. L. Simyatitskii
TMF, 1971, 6:2, 230–237

This publication is cited in the following 54 articles:

O.L. Rebenko, MATHEMATICAL FOUNDATIONS OF MODERN STATISTICAL MECHANICS, 2024
Yu. Pogorelov, A. Rebenko, “Pro vіrіalnі rozkladi korelyatsіinikh funktsіi. Kanonіchnii ansambl”, Ukr. Mat. Zhurn., 75:5 (2023), 650
Yu. Pogorelov, A. Rebenko, “On Virial Expansions of Correlation Functions. Canonical Ensemble”, Ukr Math J, 75:5 (2023), 744
Sabine Jansen, “Revisiting Groeneveld's approach to the virial expansion”, Journal of Mathematical Physics, 62:2 (2021)
A. L. Rebenko, “On the Relationships between Some Approaches to the Solution of Kirkwood–Salsburg Equations”, Ukr Math J, 73:3 (2021), 447
T. C. Dorlas, A. L. Rebenko, B. Savoie, “Correlation of clusters: Partially truncated correlation functions and their decay”, Journal of Mathematical Physics, 61:3 (2020)
A. L. Kuzemsky, “Nonequilibrium statistical operator method and generalized kinetic equations”, Theoret. and Math. Phys., 194:1 (2018), 30–56
Ya. G. Sinai, Selecta: Volume II, 2010, 73
V. I. Skrypnyk, “Solutions of the Kirkwood-Salsburg equation for particles with finite-range nonpairwise repulsion”, Ukr Math J, 60:8 (2008), 1329
Martin Grothaus, Yuri G. Kondratiev, Michael Röckner, “N/V-limit for stochastic dynamics in continuous particle systems”, Probab. Theory Relat. Fields, 137:1-2 (2007), 121
D. V. Anosov, “On the contribution of N. N. Bogolyubov to the theory of dynamical systems”, Russian Math. Surveys, 49:5 (1994), 1–18
N. N. Bogolyubov (Jr.), D. P. Sankovich, “N. N. Bogolyubov and statistical mechanics”, Russian Math. Surveys, 49:5 (1994), 19–49
Yu. A. Mitropolskii, D. Ya. Petrina, “On N. N. Bogolyubov's works in classical and quantum statistical mechanics”, Ukr Math J, 45:2 (1993), 171
R. L. Dobrushin, Ya. G. Sinai, Yu. M. Sukhov, Encyclopaedia of Mathematical Sciences, 2, Dynamical Systems II, 1989, 208
V. A. Malyshev, Ya. G. Synai, “Some Works on Ergodic Theory and Mathematical Problems of Statistical Mechanics at the Department of Probability Theory of the Faculty of Mechanics and Mathematics at the MSU”, Theory Probab. Appl., 34:1 (1989), 186–193
A. L. Rebenko, “Mathematical foundations of equilibrium classical statistical mechanics of charged particles”, Russian Math. Surveys, 43:3 (1988), 65–116
Ya. G. Sinai, N. I. Chernov, “Ergodic properties of certain systems of two-dimensional discs and three-dimensional balls”, Russian Math. Surveys, 42:3 (1987), 181–207
I. G. Brankov, V. A. Zagrebnov, N. S. Tonchev, “Description of limit gibbs states for Curie–Weiss–Ising model”, Theoret. and Math. Phys., 66:1 (1986), 72–80
R. Gelerak, “Equilibrium equations for the class of continuous systems with positive-definite two-body interaction”, Theoret. and Math. Phys., 67:2 (1986), 507–517
A. V. Marchenko, L. A. Pastur, “Transmission of waves and particles through long random barriers”, Theoret. and Math. Phys., 68:3 (1986), 929–940

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

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