3 - Hydrodynamics

Summary

Hydrodynamics is deduced from the microscopic dynamics using local equilibrium probability distributions for multicomponent normal fluids and the phases of matter with broken continuous symmetries such as crystals and liquid crystals. The Nambu–Goldstone modes resulting from continuous symmetry breaking are identified at the microscopic level of description. The entropy and the entropy production are introduced within the local equilibrium approach in agreement with the second law of thermodynamics. The Green–Kubo formulas are obtained for all the transport coefficients associated with the linear response properties, including the cross-coupling effects satisfying the Onsager–Casimir reciprocal relations as a consequence of microreversibility. The boundary conditions due to the presence of interfaces are discussed, as well as the hydrodynamic long-time tails and their consequences, especially, in low-dimensional systems.