  An `open' or $(\mu,P,T)$-ensemble describes equilibrium systems whose control
parameters are chemical potential $\mu$, pressure $P$ and temperature $T$. Such
an unconstrained ensemble is seldom used for applications to standard
thermodynamic systems due to the fact that the corresponding free energy
identically vanishes as a result of the Euler relation. However, an open
ensemble is perfectly regular for the case of black holes, as the entropy is a
quasi-homogeneous function of extensive thermodynamic variables with scaling
dictated by the Smarr formula. Following a brief discussion on thermodynamics
in the open ensemble, we compute the general form of logarithmic corrections to
the entropy of a typical system, due to fluctuations in energy, thermodynamic
volume and a generic charge $N$. This is then used to obtain the exact analytic
form of the logarithmically corrected black hole entropy for charged and
rotating black holes in anti-de Sitter spacetimes.
