  We provide a consistent description of the kinetic equation with triangle
anomaly which is compatible with the entropy principle of the second law of
thermodynamics and the charge/energy-momentum conservation equations. In
general an anomalous source term is necessary to ensure that the equations for
the charge and energy-momentum conservation are satisfied and that the
correction terms of distribution functions are compatible to these equations.
The constraining equations from the entropy principle are derived for the
anomaly-induced leading order corrections to the particle distribution
functions. The correction terms can be determined for minimum number of unknown
coefficients in one charge and two charge cases by solving the constraining
equations.
