Statistical Mechanical and Thermodynamic Entropies of the Einstein-Maxwell Dilaton-Axion Black Hole

Abstract

We discuss the connection between the statistical mechanical and thermodynamic entropies due to the nonminimally coupled scalar fields on the Einstein‐Maxwell dilaton‐axion black hole spacetime. It is demonstrated that although the statistical mechanical entropy and one-loop correction to the thermodynamic entropy are equivalent for coupling j # 0, the presence of the bare pure geometrical contribution excludes the possibility to identify the statistical mechanical entropy with the thermodynamic entropy if we use the standard renormalization scheme.