Abstract:
The H-theorem is proved for generalized equations of chemical kinetics, and important physical examples of such generalizations are considered: a discrete model of the quantum kinetic equations (the Uehling–Uhlenbeck equations) and a quantum Markov process (a quantum random walk). The time means are shown to coincide with the Boltzmann extremals for these equations and for the Liouville equation.
Bibliography: 41 titles.
\Bibitem{VedAdz14}
\by V.~V.~Vedenyapin, S.~Z.~Adzhiev
\paper Entropy in the sense of Boltzmann and Poincar\'e
\jour Russian Math. Surveys
\yr 2014
\vol 69
\issue 6
\pages 995--1029
\mathnet{http://mi.mathnet.ru/eng/rm9635}
\crossref{https://doi.org/10.1070/RM2014v069n06ABEH004926}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3400555}
\zmath{https://zbmath.org/?q=an:06434611}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2014RuMaS..69..995V}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000350984400002}
\elib{https://elibrary.ru/item.asp?id=22834475}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84925329095}
Linking options:
https://www.mathnet.ru/eng/rm9635
https://doi.org/10.1070/RM2014v069n06ABEH004926
https://www.mathnet.ru/eng/rm/v69/i6/p45
This publication is cited in the following 35 articles:
V. V. Vedenyapin, D. A. Kogtenev, “O vyvode i svoistvakh uravnenii tipa Vlasova”, Preprinty IPM im. M. V. Keldysha, 2023, 020, 18 pp.
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
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
E. Prozorova, Springer Proceedings in Complexity, 13th Chaotic Modeling and Simulation International Conference, 2021, 651
Vedenyapin V., Fimin N., Chechetkin V., “the System of Vlasov-Maxwell-Einstein-Type Equations and Its Nonrelativistic and Weak Relativistic Limits”, Int. J. Mod. Phys. D, 29:1 (2020), 2050006
Vedenyapin V.V., Fimin N.N., Chechetkin V.M., “Properties of the Vlasov-Maxwell-Einstein Equations and Their Application to the Problems of General Relativity”, Gravit. Cosmol., 26:2 (2020), 173–183
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
S. A. Rashkovskiy, “Hamiltonian Thermodynamics”, Rus. J. Nonlin. Dyn., 16:4 (2020), 557–580
S. Z. Adzhiev, Ya. G. Batishcheva, V. V. Vedenyapin, Yu. A. Volkov, V. V. Kazantseva, I. V. Melikhov, M. A. Negmatov, Yu. N. Orlov, N. N. Fimin, V. M. Chechetkin, “S.K. Godunov and kinetic theory at the Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences”, Comput. Math. Math. Phys., 60:4 (2020), 610–614
V. V. Vedenyapin, S. Z. Adzhiev, Ya. G. Batischeva, Yu. A. Volkov, V. V. Kazantseva, I. V. Melikhov, Yu. N. Orlov, M. A. Negmatov, N. N. Fimin, V. M. Chechetkin, Continuum Mechanics, Applied Mathematics and Scientific Computing: Godunov's Legacy, 2020, 381
Ch. R. Kwang-Hua, “Modeling of helium flux in cosmic rays with alpha magnetic spectrometer measurements”, Vacuum, 160 (2019), 123–127
V. V. Vedenyapin, N. I. Karavaeva, O. A. Kostyuk, B. N. Chetverushkin, “Uravnenie Shredingera kak sledstvie novykh uravnenii tipa Vlasova”, Preprinty IPM im. M. V. Keldysha, 2019, 026, 11 pp.
V. V. Vedenyapin, I. S. Pershin, “Vlasov–Maxwell–Einstein equation and Einstein lambda”, Preprinty IPM im. M. V. Keldysha, 2019, 039, 17 pp.
V. V. Vedenyapin, N. S. Smirnova, “Uravneniya Eilera i Nave–Stoksa kak sledstviya uravnenii tipa Vlasova”, Preprinty IPM im. M. V. Keldysha, 2019, 041, 20 pp.
S. Z. Adzhiev, I. V. Melikhov, V. V. Vedenyapin, “Approaches to determining the kinetics for the formation of a nano-dispersed substance from the experimental distribution functions of its nanoparticle properties”, Nanosyst.-Phys. Chem. Math., 10:5 (2019), 549–563
V. V. Vedenyapin, N. N. Fimin, V. M. Chechetkin, “Equation of Vlasov–Maxwell–Einstein type and transition to a weakly relativistic approximation”, Comput. Math. Math. Phys., 59:11 (2019), 1816–1831
Victor V. Vedenyapin, Nikolai N. Fimin, Valeriy M. Chechetkin, “DERIVATION OF VLASOV-MAXWELL-EINSTEIN EQUATION AND ITS CONNECTION WITH COSMOLOGICAL LAMBDA-TERM”, Bulletin of the MSRU (Physics and Mathematics), 2019, no. 2, 24
Natalia Tkachuk, “ENTROPY-INFORMATIONAL APPROACH TO ANALYSIS OF SELF-OGRANIZATION OF BANKING SYSTEM”, EUREKA: Social and Humanities, 3 (2019), 44
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
Ch. R. Kwang-Hua, “Thermodynamic aspect in using modified Boltzmann model as an acoustic probe for URu2Si2”, Phys. B, 537 (2018), 355–359
Citation in format AMSBIB
Contact us: