Abstract:
In this paper, we prove the H-theorem for generalized chemical kinetics equations. We consider important physical examples of such a generalization: discrete models of quantum kinetic equations (Uehling–Uhlenbeck equations) and a quantum Markov process (quantum random walk). We prove that time averages coincide with Boltzmann extremals for all such equations and for the Liouville equation as well. This gives us an approach for choosing the action–angle variables in the Hamilton–Jacobi method in a non-Hamiltonian context. We propose a simple derivation of the Hamilton–Jacobi equation from the Liouville equations in the finite-dimensional case.
Document Type:
Article
UDC:517.958
Language: Russian
Citation:
V. V. Vedenyapin, S. Z. Adzhiev, V. V. Kazantseva, “Entropy in the sense of Boltzmann and Poincare, Boltzmann extremals, and the Hamilton–Jacobi method in non-Hamiltonian context”, Differential and functional differential equations, CMFD, 64, no. 1, Peoples' Friendship University of Russia, M., 2018, 37–59
\Bibitem{VedAdzKaz18}
\by V.~V.~Vedenyapin, S.~Z.~Adzhiev, V.~V.~Kazantseva
\paper Entropy in the sense of Boltzmann and Poincare, Boltzmann extremals, and the Hamilton--Jacobi method in non-Hamiltonian context
\inbook Differential and functional differential equations
\serial CMFD
\yr 2018
\vol 64
\issue 1
\pages 37--59
\publ Peoples' Friendship University of Russia
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd345}
\crossref{https://doi.org/10.22363/2413-3639-2018-64-1-37-59}
Linking options:
https://www.mathnet.ru/eng/cmfd345
https://www.mathnet.ru/eng/cmfd/v64/i1/p37
This publication is cited in the following 6 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, V. I. Parenkina, A. G. Petrov, Chzhan Khaochen, “Uravnenie Vlasova-Einshteina i tochki Lagranzha”, Preprinty IPM im. M. V. Keldysha, 2022, 023, 23 pp.
V. V. Vedenyapin, N. N. Fimin, V. M. Chechetkin, “Properties of the vlasov-maxwell-einstein equations and their application to the problems of general relativity”, Gravit. Cosmol., 26:2 (2020), 173–183
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
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.
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