  We work on the relation between the local thermodynamic instability and the
dynamical instability of large black holes in four-dimensional anti-de Sitter
space proposed by Gubser and Mitra. We find that all perturbations suppressing
the metric fluctuations at linear order become dynamically unstable when black
holes lose the local thermodynamic stability. We discuss how dynamical
instabilities can be explained by the Second Law of Thermodynamics.
