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An `open' or $(\mu,P,T)$-ensemble describes equilibrium systems whose controlparameters are chemical potential $\mu$, pressure $P$ and temperature $T$. Suchan unconstrained ensemble is seldom used for applications to standardthermodynamic systems due to the fact that the corresponding free energyidentically vanishes as a result of the Euler relation. However, an openensemble is perfectly regular for the case of black holes, as the entropy is aquasi-homogeneous function of extensive thermodynamic variables with scalingdictated by the Smarr formula. Following a brief discussion on thermodynamicsin the open ensemble, we compute the general form of logarithmic corrections tothe entropy of a typical system, due to fluctuations in energy, thermodynamicvolume and a generic charge $N$. This is then used to obtain the exact analyticform of the logarithmically corrected black hole entropy for charged androtating black holes in anti-de Sitter spacetimes.

Logarithmic corrections to the entropy function of black holes in the open ensemble