Uspekhi Matematicheskikh Nauk
General information
Latest issue
Impact factor
License agreement
Submit a manuscript

Search papers
Search references

Latest issue
Current issues
Archive issues
What is RSS

Uspekhi Mat. Nauk:

Personal entry:
Save password
Forgotten password?

Uspekhi Mat. Nauk, 2008, Volume 63, Issue 1(379), Pages 3–36 (Mi umn8517)  

This article is cited in 19 scientific papers (total in 19 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

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.


Full text: PDF file (708 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 2008, 63:1, 1–34

Bibliographic databases:

UDC: 519.2
MSC: Primary 60K30, 80A30; Secondary 60J27, 82C22, 82C40, 82C43, 92E20
Received: 04.09.2007

Citation: V. A. Malyshev, S. A. Pirogov, “Reversibility and irreversibility in stochastic chemical kinetics”, Uspekhi Mat. Nauk, 63:1(379) (2008), 3–36; Russian Math. Surveys, 63:1 (2008), 1–34

Citation in format AMSBIB
\by V.~A.~Malyshev, S.~A.~Pirogov
\paper Reversibility and irreversibility in stochastic chemical kinetics
\jour Uspekhi Mat. Nauk
\yr 2008
\vol 63
\issue 1(379)
\pages 3--36
\jour Russian Math. Surveys
\yr 2008
\vol 63
\issue 1
\pages 1--34

Linking options:

    SHARE: FaceBook Twitter Livejournal

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

    This publication is cited in the following articles:
    1. V. A. Malyshev, “On mathematical models of the service networks”, Autom. Remote Control, 70:12 (2009), 1947–1953  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    2. Ao Ping, “Global view of bionetwork dynamics: adaptive landscape”, Journal of Genetics and Genomics, 36:2 (2009), 63–73  crossref  mathscinet  isi  elib  scopus
    3. S. Z. Adzhiev, V. V. Vedenyapin, “Time averages and Boltzmann extremals for Markov chains, discrete Liouville equations, and the Kac circular model”, Comput. Math. Math. Phys., 51:11 (2011), 1942–1952  mathnet  crossref  mathscinet  isi
    4. Gasnikov A.V., Gasnikova E.V., Fedko O.S., “O vozmozhnoi dinamike v modeli ranzhirovaniya web-stranits PageRank i modernizirovannoi modeli rascheta matritsy korrespondentsii”, Tr. Moskovskogo fiziko-tekhnicheskogo instituta, 4:2(14) (2012), 101–120  elib
    5. A. V. Gasnikov, E. V. Gasnikova, “On Entropy-Type Functionals Arising in Stochastic Chemical Kinetics Related to the Concentration of the Invariant Measure and Playing the Role of Lyapunov Functions in the Dynamics of Quasiaverages”, Math. Notes, 94:6 (2013), 854–861  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    6. V. V. Vedenyapin, S. Z. Adzhiev, “Entropy in the sense of Boltzmann and Poincaré”, Russian Math. Surveys, 69:6 (2014), 995–1029  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    7. Gertsik V.M., “Asymptotic Independence For Stationary State of Mean Field Markov Process”, Markov Process. Relat. Fields, 20:2 (2014), 375–380  mathscinet  zmath  isi
    8. 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
    9. 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
    10. 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
    11. 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
    12. 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
    13. 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
    14. 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
    15. 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
    16. 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
    17. 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
    18. 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
    19. 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
  • Успехи математических наук Russian Mathematical Surveys
    Number of views:
    This page:1078
    Full text:415
    First page:31

    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021