  We investigate thermodynamic and dynamical stability of a family of
six-dimensional braneworld solutions with de Sitter branes. First, we
investigate thermodynamic stability in terms of de Sitter entropy. We see that
the family of solutions is divided into two distinct branches: the high-entropy
branch and the low-entropy branch. By analogy with ordinary thermodynamics, the
high-entropy branch is expected to be stable and the low-entropy branch to be
unstable. Next, we investigate dynamical stability by analyzing linear
perturbations around the solutions. Perturbations are decomposed into scalar,
vector and tensor sectors according to the representation of the 4D de Sitter
symmetry, and each sector is analyzed separately. It is found that when the
Hubble expansion rates on the branes are too large, there appears a tachyonic
mode in the scalar sector and the background solution becomes dynamically
unstable. We show analytically that the onset of the thermodynamic instability
and that of the dynamical instability exactly coincide. Therefore, the
braneworld model provides a new example illustrating close relations between
thermodynamic and dynamical instability.
