Thermodynamic phase transitions from dynamical compact dimensions

We perform a double quotient of global AdS${}_4$ and study its thermal properties. We find that a double quotient yields a spacetime with an expanding compact dimension. Studying the entanglement of the dual CFT we find that, at early times, the spacetime has thermal properties which disappear after a critical time. For slow expansion, this critical time depends on the expansion rate as expected, but becomes much more sensitive with more rapid expansion rates.