  We construct the general hydrodynamic description of (3+1)-dimensional chiral
charged (quantum) fluids subject to a strong external magnetic field with
effective field theory methods. We determine the constitutive equations for the
energy-momentum tensor and the axial charge current, in part from a generating
functional. Furthermore, we derive the Kubo formulas which relate two-point
functions of the energy-momentum tensor and charge current to 27 transport
coefficients: 8 independent thermodynamic, 4 independent non-dissipative
hydrodynamic, and 10 independent dissipative hydrodynamic transport
coefficients. Five Onsager relations render 5 more transport coefficients
dependent. We uncover four novel transport effects, which are encoded in what
we call the shear-induced conductivity, the two expansion-induced longitudinal
conductivities and the shear-induced Hall conductivity. Remarkably, the
shear-induced Hall conductivity constitutes a novel non-dissipative transport
effect. As a demonstration, we compute all transport coefficients explicitly in
a strongly coupled quantum fluid via holography.
