Statistical mechanical and thermodynamic entropies of the Einstein-Maxwelldilaton-axion black hole

We discuss the connection between the statistical mechanical and thermodyna mic entropies due to the nonminimally coupled scalar fields on the Einstein -Maxwell dilaton-axion black hole spacetime. It is demonstrated that althou gh the statistical mechanical entropy and one-loop correction to the thermo dynamic entropy are equivalent for coupling xi less than or equal to 0, the presence of the bare pure geometrical contribution excludes the possibilit y to identify the statistical mechanical entropy with the thermodynamic ent ropy if we use the standard renormalization scheme.