Abstract:
Time averages are proved to coincide with Boltzmann extremals for Markov chains, discrete Liouville equations, and their generalizations. A variational principle is proposed for finding stationary solutions in these cases.
Citation:
S. Z. Adzhiev, V. V. Vedenyapin, “Time averages and Boltzmann extremals for Markov chains, discrete Liouville equations, and the Kac circular model”, Zh. Vychisl. Mat. Mat. Fiz., 51:11 (2011), 2063–2074; Comput. Math. Math. Phys., 51:11 (2011), 1942–1952
\Bibitem{AdzVed11}
\by S.~Z.~Adzhiev, V.~V.~Vedenyapin
\paper Time averages and Boltzmann extremals for Markov chains, discrete Liouville equations, and the Kac circular model
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2011
\vol 51
\issue 11
\pages 2063--2074
\mathnet{http://mi.mathnet.ru/zvmmf9576}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2933115}
\transl
\jour Comput. Math. Math. Phys.
\yr 2011
\vol 51
\issue 11
\pages 1942--1952
\crossref{https://doi.org/10.1134/S0965542511110029}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000297345000010}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-81455148960}
Linking options:
https://www.mathnet.ru/eng/zvmmf9576
https://www.mathnet.ru/eng/zvmmf/v51/i11/p2063
This publication is cited in the following 25 articles:
V.V. Vedenyapin, A.A. Bay, V.I. Parenkina, A.G. Petrov, “Minimal Action Principle for Gravity and Electrodynamics, Einstein Lambda, and Lagrange Points”, Markov Processes And Related Fields, 2024, no. 2023 №4(29), 515
V. V. Vedenyapin, A. A. Bay, “Least action principle for gravity and electrodynamics, the Lambda-term and the analog of Milne–McCrea solution for Lorentzian metric”, Eur. Phys. J. Plus, 139:2 (2024)
V. V. Vedenyapin, V. I. Parenkina, A. G. Petrov, Chzhan Khaochen, “Uravnenie Vlasova-Einshteina i tochki Lagranzha”, Preprinty IPM im. M. V. Keldysha, 2022, 023, 23 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
V. V. Vedenyapin, V. I. Parenkina, S. R. Svirshchevskii, “Derivation of the equations of electrodynamics and gravity from the principle of least action”, Comput. Math. Math. Phys., 62:6 (2022), 983–995
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. 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, 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.
Adzhiev S.Z. Melikhov V I. Vedenyapin V.V., “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
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
V. V. Vedenyapin, T. S. Kazakova, Ya. K. V., B. N. Chetverushkin, “Schrödinger equation as a self-consistent field”, Dokl. Math., 97:3 (2018), 240–242
V. V. Vedenyapin, A. A. Andreeva, V. V. Vorobyeva, “Euler and Navier–Stokes equations as self-consistent fields”, Dokl. Math., 97:3 (2018), 283–285
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
V. V. Vedenyapin, “Uravnenie Vlasova–Maksvella–Einshteina”, Preprinty IPM im. M. V. Keldysha, 2018, 188, 20 pp.
V. V. Vedenyapin, N. N. Fimin, V. M. Chechetkin, “Ob uravnenii Vlasova–Maksvella–Einshteina i ego nerelyativistskikh i slaborelyativistskikh analogakh”, Preprinty IPM im. M. V. Keldysha, 2018, 265, 30 pp.
V. V. Vedenyapin, M. A. Negmatov, N. N. Fimin, “Vlasov-type and Liouville-type equations, their microscopic, energetic and hydrodynamical consequences”, Izv. Math., 81:3 (2017), 505–541
Citation in format AMSBIB
Contact us: