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Résumé |
In phases of condensed matter with broken continuous symmetries, as well as in fluids, transport processes
generate irreversibility at the macroscale. To be complete, the hydrodynamic equations must include these
dissipative effects. A fundamental question is to deduce all of them from the microscopic Hamiltonian
dynamics of the particles with the methods of non-equilibrium statistical mechanics. In this presentation, a
first-principle derivation based on a local-equilibrium approach is introduced. As an example of application,
the crystalline solid is considered. The breaking of the three-dimensional continuous group of spatial
translations implies the existence of three slow modes in addition to the five slow modes arising from the
fundamental conservation laws of mass, energy, and linear momentum. Finally, based on the results of the
local-equilibrium approach, the equilibrium and nonequilibrium properties relevant to the hydrodynamics of
the perfect hard-sphere crystal are obtained with molecular dynamics simulations. |
