Nernst theorem and entropy of the axisymmetric Einstein-Maxwell-Dilaton-axion black hole

The free energy and the entropy of scalar field are calculated by brick-wall in the axisymmetric Einstein-Maxwell-Dilaton-axion black hole. It is shown that when the black hole has inner and outer horizons, the entropy is not only related to the area of an outer horizon but also is the function of the area of an inner horizon. When the area of an inner horizon approaches zero, we can obtain the known conclusion. The entropy expressed by location parameter of outer horizon and inner horizons approaches absolute zero. It obeys Nernst theorem. It can be taken as Planck absolute entropy of a black hole.