  By using the 't Hooft "brick wall" model and the Pauli-Villars regularization
scheme we calculate the statistical-mechanical entropy arising from the
minimally coupled scalar fields which rotate with the azimuthal angular
velocity $\Omega_0=\Omega_H$ ($\Omega_H$ is the angular velocity of the black
hole horizon) in the general four-dimensional non-extreme stationary
axisymmetric black hole space-time. We also show, for the Kerr-Newman and the
Einstein-Maxwell dilaton-axion black holes, that the statistical-mechanical
entropy obtained from our derivation and the quantum thermodynamical entropy by
the conical singularity method are equivalent.
