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Russian Mathematical Surveys, 2008, Volume 63, Issue 1, Pages 1–34
DOI: https://doi.org/10.1070/RM2008v063n01ABEH004500
(Mi rm8517)
 

This article is cited in 28 scientific papers (total in 28 papers)

Reversibility and irreversibility in stochastic chemical kinetics

V. A. Malysheva, S. A. Pirogovb

a M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b Institute for Information Transmission Problems, Russian Academy of Sciences
References:
Abstract: Mathematical models with mean field and local type interaction are considered in connection with stochastic chemical kinetics. Special emphasis is placed on various notions of reversibility, their consequences (Boltzmann type equations, fluctuations, Onsager relations, and so on), and the emergence of irreversibility.
Received: 04.09.2007
Bibliographic databases:
Document Type: Article
UDC: 519.2
MSC: Primary 60K30, 80A30; Secondary 60J27, 82C22, 82C40, 82C43, 92E20
Language: English
Original paper language: Russian
Citation: V. A. Malyshev, S. A. Pirogov, “Reversibility and irreversibility in stochastic chemical kinetics”, Russian Math. Surveys, 63:1 (2008), 1–34
Citation in format AMSBIB
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\paper Reversibility and irreversibility in stochastic chemical kinetics
\jour Russian Math. Surveys
\yr 2008
\vol 63
\issue 1
\pages 1--34
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Linking options:
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  • This publication is cited in the following 28 articles:
    1. Evgenia Gasnikova, Alexander Gasnikov, Yaroslav Kholodov, Anastasiya Zukhba, “An Evolutionary View on Equilibrium Models of Transport Flows”, Mathematics, 11:4 (2023), 858  crossref
    2. V. V. Vedenyapin, S. Z. Adzhiev, V. V. Kazantseva, “Boltzmann and Poincaré Entropy, Boltzmann Extremals, and Hamilton–Jacobi Method for Non-Hamiltonian Situation”, J Math Sci, 260:4 (2022), 434  crossref
    3. S. Z. Adzhiev, V. V. Vedenyapin, I. V. Melikhov, “Kinetic aggregation models leading to morphological memory of formed structures”, Comput. Math. Math. Phys., 62:2 (2022), 254–268  mathnet  mathnet  crossref  crossref  isi  scopus
    4. Ya. G. Batishcheva, “Cauchy problem for a new aggregation–fragmentation model in the case of equal reaction rate constants”, Comput. Math. Math. Phys., 62:3 (2022), 452–466  mathnet  mathnet  crossref  crossref  isi  scopus
    5. A. S. Ivanova, S. S. Omelchenko, E. V. Kotlyarova, V. V. Matyukhin, “Kalibrovka parametrov modeli rascheta matritsy korrespondentsii dlya g. Moskvy”, Kompyuternye issledovaniya i modelirovanie, 12:5 (2020), 961–978  mathnet  crossref
    6. Adzhiev S.Z. Melikhov V I. Vedenyapin V.V., “On the H-Theorem For the Becker-Doring System of Equations For the Cases of Continuum Approximation and Discrete Time”, Physica A, 553 (2020), 124608  crossref  mathscinet  isi
    7. E. N. Petrova, S. A. Pirogov, “What is time reversal?”, Mosc. Math. J., 20:4 (2020), 813–816  mathnet  crossref
    8. D. R. Baymurzina, A. V. Gasnikov, E. V. Gasnikova, P. E. Dvurechenskii, E. I. Ershov, M. B. Kubentayeva, A. A. Lagunovskaya, “Universal method of searching for equilibria and stochastic equilibria in transportation networks”, Comput. Math. Math. Phys., 59:1 (2019), 19–33  mathnet  crossref  crossref  isi  elib
    9. Sergey Adzhiev, Janina Batishcheva, Igor Melikhov, Victor Vedenyapin, “Kinetic Equations for Particle Clusters Differing in Shape and the H-theorem”, Physics, 1:2 (2019), 229  crossref
    10. A. Gasnikov, P. Dvurechensky, M. Zhukovskii, S. Kim, S. Plaunov, D. Smirnov, F. Noskov, “About the power law of the PageRank vector distribution. Part 2. Backley–Osthus model, power law verification for this model and setup of real search engines”, Num. Anal. Appl., 11:1 (2018), 16–32  mathnet  crossref  crossref  isi  elib
    11. V. V. Vedenyapin, S. Z. Adzhiev, V. V. Kazantseva, “Entropiya po Boltsmanu i Puankare, ekstremali Boltsmana i metod Gamiltona–Yakobi v negamiltonovoi situatsii”, Differentsialnye i funktsionalno-differentsialnye uravneniya, SMFN, 64, no. 1, Rossiiskii universitet druzhby narodov, M., 2018, 37–59  mathnet  crossref
    12. A. Gasnikov, E. Gasnikova, P. Dvurechensky, A. Mohammed, E. Chernousova, “About the power law of the PageRank vector distribution. Part 1. Numerical methods for finding the PageRank vector”, Num. Anal. Appl., 10:4 (2017), 299–312  mathnet  crossref  crossref  isi  elib
    13. Adzhiev S.Z. Melikhov I.V. Vedenyapin V.V., “The H-Theorem For the Physico-Chemical Kinetic Equations With Explicit Time Discretization”, Physica A, 481 (2017), 60–69  crossref  mathscinet  isi  scopus
    14. S. Z. Adzhiev, I. V. Melikhov, V. V. Vedenyapin, “The H-theorem for the physico-chemical kinetic equations with discrete time and for their generalizations”, Phys. A, 480 (2017), 39–50  crossref  mathscinet  isi  scopus
    15. S. Adzhiev, I. Melikhov, V. Vedenyapin, “The H-Theorem For the Chemical Kinetic Equations With Discrete Time and For Their Generalizations”, V International Conference on Problems of Mathematical and Theoretical Physics and Mathematical Modelling, Journal of Physics Conference Series, 788, IOP Publishing Ltd, 2017, UNSP 012001  crossref  isi  scopus
    16. S. Z. Adzhiev, V. V. Vedenyapin, Yu. A. Volkov, I. V. Melikhov, “Generalized Boltzmann-type equations for aggregation in gases”, Comput. Math. Math. Phys., 57:12 (2017), 2017–2029  mathnet  crossref  crossref  isi  elib
    17. A. V. Gasnikov, E. V. Gasnikova, Yu. E. Nesterov, A. V. Chernov, “Efficient numerical methods for entropy-linear programming problems”, Comput. Math. Math. Phys., 56:4 (2016), 514–524  mathnet  crossref  crossref  mathscinet  isi  elib
    18. A. V. Gasnikov, E. V. Gasnikova, M. A. Mendel, K. V. Chepurchenko, “Evolyutsionnye vyvody entropiinoi modeli rascheta matritsy korrespondentsii”, Matem. modelirovanie, 28:4 (2016), 111–124  mathnet  elib
    19. Pirogov S. Rybko A. Kalinina A. Gelfand M., “Recombination Processes and Nonlinear Markov Chains”, J. Comput. Biol., 23:9 (2016), 711–717  crossref  mathscinet  isi  elib  scopus
    20. Alvise Bastianello, Spyros Sotiriadis, “Cluster expansion for ground states of local Hamiltonians”, Nuclear Physics B, 909 (2016), 1020  crossref
    Citing articles in Google Scholar: Russian citations, English citations
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