  We provide a complete derivation of hydrodynamic equations for
nonrelativistic systems based on quantum field theories of spinless
Schr\"odeinger fields, assuming that an initial density operator takes a
special form of the local Gibbs distribution. The constructed
optimized/renormalized perturbation theory for real-time evolution enables us
to separately evaluate dissipative and nondissipative parts of constitutive
relations. It is shown that the path-integral formula for local thermal
equilibrium together with the symmetry properties of the resulting action---the
nonrelativistic diffeomorphism and gauge symmetry in the thermally emergent
Newton-Cartan geometry---provides a systematic way to derive the nondissipative
part of constitutive relations. We further show that dissipative parts are
accompanied with the entropy production operator together with two kinds of
fluctuation theorems by the use of which we derive the dissipative part of
constitutive relations and the second law of thermodynamics. After obtaining
the exact expression for constitutive relations, we perform the derivative
expansion and derive the first-order hydrodynamic (Navier-Stokes) equation with
the Green-Kubo formula for transport coefficients.
