Sommaire:

Transport processes generating irreversibility at the macroscale, the hydrodynamic equations must include these dissipative effects to be complete. The hydrodynamic modes stem from the fundamental conservation laws and from the breaking of continuous symmetries. A key question is to deduce the dissipative hydrodynamic equations ruling all these modes 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 illustrative example, 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. Based on the results of the local-equilibrium approach, the equilibrium and nonequilibrium properties relevant to the dissipative hydrodynamics of the hard-sphere crystal are obtained with molecular dynamics simulations. Finally, the application of the method to amorphous solids and active matter systems is discussed.

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