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

This article is cited in 10 scientific papers (total in 10 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.

DOI: https://doi.org/10.4213/rm8517

Full text: PDF file (708 kB)
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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
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    Citing articles on Google Scholar: Russian citations, English citations
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    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
    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  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
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