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

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 str...

Full description

Saved in:
Bibliographic Details
Published in:Theoretical and mathematical physics 2009-02, Vol.158 (2), p.233-245
Main Authors: Kovalevskii, M. Yu, Matskevich, V. T., Razumnyi, A. Ya
Format: Article
Language:English
Subjects:
Applications of Mathematics
Mathematical and Computational Physics
Physics
Physics and Astronomy
Theoretical
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0040-5779
1573-9333
DOI:10.1007/s11232-009-0019-1