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.

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