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Holographic studies of the entanglement entropy of field theories dual tocharged and neutral black holes in asymptotically global AdS4 spacetimes arepresented. The goal is to elucidate various properties of the quantity that arepeculiar to working in finite volume, and to gain access to the behaviour ofthe entanglement entropy in the rich thermodynamic phase structure that ispresent at finite volume and large N. The entropy is followed through variousfirst order phase transitions, and also a novel second order phase transition.Properties of a specific heat in the neighbourhood of the critical point arecomputed. Behaviour is found that contrasts interestingly with an earlierholographic study of a second order phase transition dual to an holographicsuperconductor.

Large N Phase Transitions, Finite Volume, and Entanglement Entropy