Thermodynamic instability of dark energy equation of state

We derive the dark energy fluid equation of state $P=-\epsilon =\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}\mathrm{.}$ as an extremum of entropy, subject to the Hamiltonian constraint of General Relativity. However, we identify perturbations that can render this extremum an entropy minimum designating a thermodynamic instability and specify the mathematical condition for this to occur.