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CMFD, 2018, Volume 64, Issue 1, Pages 37–59 (Mi cmfd345)  

This article is cited in 1 scientific paper (total in 1 paper)

Entropy in the sense of Boltzmann and Poincare, Boltzmann extremals, and the Hamilton–Jacobi method in non-Hamiltonian context

V. V. Vedenyapina, S. Z. Adzhievb, V. V. Kazantsevaa

a Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences, Moscow, Russia
b Lomonosov Moscow State University, Moscow, Russia

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.

DOI: https://doi.org/10.22363/2413-3639-2018-64-1-37-59

Full text: PDF file (266 kB)
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UDC: 517.958

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

Citation in format AMSBIB
\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}


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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. 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.  mathnet  crossref
  • Современная математика. Фундаментальные направления
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