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Teoreticheskaya i Matematicheskaya Fizika, 2009, Volume 158, Number 2, Pages 277–291
DOI: https://doi.org/10.4213/tmf6314 (Mi tmf6314) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Universality of the relaxation structure of equations for the dynamics of continuous media and dissipative Poisson brackets

M. Yu. Kovalevskyab, V. T. Matskevichb, A. Ya. Razumnyic

a Belgorod State University
b National Science Centre Kharkov Institute of Physics and Technology
c V. N. Karazin Kharkiv National University
Full-text PDF (404 kB) Citations (2)
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DOI: https://doi.org/10.4213/tmf6314
Abstract: We generalize the Hamilton equations for dynamical processes with relaxation. We introduce a dissipative Poisson bracket in terms of the dissipation function. We obtain the universal structure of the relaxation terms in the equations for the dynamics of condensed media and verify this result for structureless liquids, elastic solids, and quantum liquids. In the examples of the condensed media under consideration, we obtain expressions for the dissipative Poisson brackets for the complete set of dynamical parameters.
Keywords: Hamiltonian approach, entropy, dissipative Poisson bracket, kinetic coefficient, solid, quantum liquid, dissipation function.
Received: 10.01.2008
Revised: 10.04.2008
English version:
Theoretical and Mathematical Physics, 2009, Volume 158, Issue 2, Pages 233–245
DOI: https://doi.org/10.1007/s11232-009-0019-1
Bibliographic databases:
Language: Russian
Citation: M. Yu. Kovalevsky, V. T. Matskevich, A. Ya. Razumnyi, “Universality of the relaxation structure of equations for the dynamics of continuous media and dissipative Poisson brackets”, TMF, 158:2 (2009), 277–291; Theoret. and Math. Phys., 158:2 (2009), 233–245
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf6314
  • https://doi.org/10.4213/tmf6314
  • https://www.mathnet.ru/eng/tmf/v158/i2/p277
    • This publication is cited in the following 2 articles:
    1. Kovalevsky M.Y., Kotelnikova O.A., “Symmetry, Phase States and Dynamics of Magnets With Spin S=1”, Problems of Atomic Science and Technology, 2012, no. 1, 316–320  isi
    2. M. Yu. Kovalevsky, “The $SU(3)$ symmetry and macroscopic dynamics of magnets with spin $s=1$”, Theoret. and Math. Phys., 168:2 (2011), 1064–1077  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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    Abstract page:669
    Full-text PDF :248
    References:105
    First page:11
     
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