For a thermodynamic system, apart from thermal fluctuations, there are also
fluctuations in thermodynamic volume when the system is in contact with a
volume reservoir. For the case of black holes in anti-de Sitter spacetimes, the
effect of thermal fluctuations on the entropy is well studied. The aim of this
work is to compute novel logarithmic corrections to black hole entropy coming
from simultaneous fluctuations of energy and thermodynamic volume. We work in
the isothermal-isobaric ensemble and first obtain a general form of corrections
to entropy which are valid for any thermodynamic system. Applying the formalism
to Kerr black holes in AdS reveals that the black hole entropy gets corrected
as: $\mathcal{S} = S_0 – k \ln S_0 + \cdots$ where $S_0$ is given by the
Bekenstein-Hawking formula and $k = – 1$. The same leading coefficient is also
obtained in the canonical ensemble, i.e. by considering energy fluctuations
alone. This coefficient is found to be unaltered in the slowly rotating and
high temperature limits.
