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 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.