  It is shown that a Quantum Isolated Horizon(QIH), as observed by a local
observer, is locally unstable as a thermodynamic system. The result is derived
in two different ways. Firstly, the specific heat of the QIH is shown to be
negative definite through a quantum statistical analysis. Then, it is shown, in
the thermal holographic approach, that the canonical partition function of the
QIH diverges under Gaussian thermal fluctuations of such energy spectrum,
implying local instability of such a QIH as a thermodynamic system.
