Abstract. Using quantum statistical method, we obtain the partition function of Bose field and Fermi field on the background of the axisymmetrical NUT-Kerr-Newman black hole. The difficult to solve wave equation is avoided. Then via the membrane model we calculate the entropy of Bose field and Fermi field of the black hole. Though discussing, we derive that the black hole's entropy consists of two parts. According to the property that the entropy is an extensive quantity, we know that the entropy is the contribution of two thermodynamic systems. On this basis, a new Bekenstein-Smarr formula is given. It is shown that the entropy expressed by two thermodynamic systems will approach zero, when the radiation temperature approaches absolute zero.It satisfies Nernst theorem. The entropy can be taken as the Planck absolute entropy.

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