Novel Aspects of the Extended First Law of Entanglement

Understand

Using AdS/CFT an extended first law of entanglement has been previously derived for the vacuum reduced to a ball in Minkowski.

• The statement not only includes perturbations of the state but also of the conformal field theory (CFT), via variations of the generalized central charge.
• We clarify some subtleties previously overlooked and use simple arguments to generalize prior derivations to arbitrary gravity theories in the bulk as well as new regions in the boundary CFT.
• Our construction also applies to two-dimensional bulk theories and admits an interesting extension for a three-dimensional bulk, providing a curious result regarding the thermodynamic volume in extended black hole thermodynamics.