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TMF, 2009, Volume 158, Number 2, Pages 277–291 (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

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

DOI: https://doi.org/10.4213/tmf6314

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English version:
Theoretical and Mathematical Physics, 2009, 158:2, 233–245

Bibliographic databases:

Received: 10.01.2008
Revised: 10.04.2008

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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\paper Universality of the~relaxation structure of equations for the~dynamics of continuous media and dissipative Poisson brackets
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  • http://mi.mathnet.ru/eng/tmf/v158/i2/p277

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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. 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
    2. 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
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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