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We consider time-dependent entanglement entropy (EE) for a 1+1 dimensionalCFT in the presence of angular momentum and U(1) charge. The EE saturates,irrespective of the initial state, to the grand canonical entropy after a timelarge compared with the length of the entangling interval. We reproduce the CFTresults from an AdS dual consisting of a spinning BTZ black hole and a flatU(1) connection. The apparent discrepancy that the holographic EE does not apriori depend on the U(1) charge while the CFT EE does, is resolved by thecharge-dependent shift between the bulk and boundary stress tensors. We showthat for small entangling intervals, the entanglement entropy obeys the firstlaw of thermodynamics, as conjectured recently. The saturation of the EE in thefield theory is shown to follow from a version of quantum ergodicity; thederivation indicates that it should hold for conformal as well as massivetheories in any number of dimensions.

Dynamical entanglement entropy with angular momentum and U(1) charge