  The macroscopic hydrodynamic equations are derived for many-body systems in
the local-equilibrium approach, using the Schr\"odinger picture of quantum
mechanics. In this approach, statistical operators are defined in terms of
microscopic densities associated with the fundamentally conserved quantities
and other slow modes possibly emerging from continuous symmetry breaking, as
well as macrofields conjugated to these densities. Functional identities can be
deduced, allowing us to identify the reversible and dissipative parts of the
mean current densities, to obtain general equations for the time evolution of
the conjugate macrofields, and to establish the relationship to
projection-operator methods. The entropy production is shown to be nonnegative
by applying the Peierls-Bogoliubov inequality to a quantum integral fluctuation
theorem. Using the expansion in the gradients of the conjugate macrofields, the
transport coefficients are given by Green-Kubo formulas and the entropy
production rate can be expressed in terms of quantum Einstein-Helfand formulas,
implying its nonnegativity in agreement with the second law of thermodynamics.
The results apply to multicomponent fluids and can be extended to condensed
matter phases with broken continuous symmetries.
