V. V. Kozlov, D. V. Treschev, “Weak Convergence of Solutions of the Liouville Equation for Nonlinear Hamiltonian Systems”, TMF, 134:3 (2003), 388–400; Theoret. and Math. Phys., 134:3 (2003), 339

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Teoreticheskaya i Matematicheskaya Fizika, 2003, Volume 134, Number 3, Pages 388–400
DOI: https://doi.org/10.4213/tmf164 (Mi tmf164)

This article is cited in 34 scientific papers (total in 34 papers)

Weak Convergence of Solutions of the Liouville Equation for Nonlinear Hamiltonian Systems

V. V. Kozlov, D. V. Treschev

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Full-text PDF (262 kB) Citations (34)

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DOI: https://doi.org/10.4213/tmf164

Abstract: We suggest sufficient conditions for the existence of weak limits of solutions of the Liouville equation as time increases indefinitely. The presence of the weak limit of the probability distribution density leads to a new interpretation of the second law of thermodynamics for entropy increase.

Keywords: Hamiltonian system, Liouville equation, weak convergence, entropy.

Received: 05.07.2002

English version:
Theoretical and Mathematical Physics, 2003, Volume 134, Issue 3, Pages 339–350
DOI: https://doi.org/10.1023/A:1022697321418

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: V. V. Kozlov, D. V. Treschev, “Weak Convergence of Solutions of the Liouville Equation for Nonlinear Hamiltonian Systems”, TMF, 134:3 (2003), 388–400; Theoret. and Math. Phys., 134:3 (2003), 339–350

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/tmf164

https://doi.org/10.4213/tmf164

https://www.mathnet.ru/eng/tmf/v134/i3/p388

This publication is cited in the following 34 articles:

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A. S. Trushechkin, M. Merkli, J. D. Cresser, J. Anders, “Open quantum system dynamics and the mean force Gibbs state”, AVS Quantum Sci., 4 (2022), 12301–23
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A. I. Komech, E. A. Kopylova, “Attractors of nonlinear Hamiltonian partial differential equations”, Russian Math. Surveys, 75:1 (2020), 1–87
Valery V. Kozlov, “Nonequilibrium Statistical Mechanics of Weakly Ergodic Systems”, Regul. Chaotic Dyn., 25:6 (2020), 674–688
Qian H., Wang Sh., Yi Y., “Entropy Productions in Dissipative Systems”, Proc. Amer. Math. Soc., 147:12 (2019), 5209–5225
Carati A., Galgani L., Gangemi F., Gangemi R., “Relaxation Times and Ergodic Properties in a Realistic Ionic-Crystal Model, and the Modern Form of the Fpu Problem”, Physica A, 532 (2019), UNSP 121911
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
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Tatiana Salnikova, Vsevolod Salnikov, 2018 14th International Conference “Stability and Oscillations of Nonlinear Control Systems” (Pyatnitskiy's Conference) (STAB), 2018, 1
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
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
Adzhiev S.Z., Melikhov I.V., Vedenyapin V.V., “The H-Theorem For the Physico-Chemical Kinetic Equations With Discrete Time and For Their Generalizations”, Physica A, 480 (2017), 39–50
Adzhiev S., Melikhov I., Vedenyapin V., “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
V. V. Kozlov, “Polynomial conservation laws for the Lorentz gas and the Boltzmann–Gibbs gas”, Russian Math. Surveys, 71:2 (2016), 253–290
Lykov A.A., Malyshev V.A., “a New Approach To Boltzmann'S Ergodic Hypothesis”, Dokl. Math., 92:2 (2015), 624–626
V. V. Vedenyapin, S. Z. Adzhiev, “Entropy in the sense of Boltzmann and Poincaré”, Russian Math. Surveys, 69:6 (2014), 995–1029
Trushechkin A., “Microscopic and Soliton-Like Solutions of the Boltzmann Enskog and Generalized Enskog Equations For Elastic and Inelastic Hard Spheres”, Kinet. Relat. Mod., 7:4 (2014), 755–778
I. V. Volovich, A. S. Trushechkin, “Asymptotic properties of quantum dynamics in bounded domains at various time scales”, Izv. Math., 76:1 (2012), 39–78

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

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