  The second-order nonlinear responses of inviscid chiral fluids near local
equilibrium are investigated by applying the chiral kinetic theory (CKT)
incorporating side-jump effects. It is shown that the local equilibrium
distribution function can be non-trivially introduced in a co-moving frame with
respect to the fluid velocity when the quantum corrections in collisions are
involved. For the study of anomalous transport, contributions from both quantum
corrections in anomalous hydrodynamic equations of motion and those from the
CKT and Wigner functions are considered under the relaxation-time (RT)
approximation, which result in anomalous charge Hall currents propagating along
the cross product of the background electric field and the temperature (or
chemical-potential) gradient and of the temperature and chemical-potential
gradients. On the other hand, the nonlinear quantum correction on the charge
density vanishes in the classical RT approximation, which in fact satisfies the
matching condition given by the anomalous equation obtained from the CKT.
