  We consider time-dependent entanglement entropy (EE) for a 1+1 dimensional
CFT 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 time
large compared with the length of the entangling interval. We reproduce the CFT
results from an AdS dual consisting of a spinning BTZ black hole and a flat
U(1) connection. The apparent discrepancy that the holographic EE does not a
priori depend on the U(1) charge while the CFT EE does, is resolved by the
charge-dependent shift between the bulk and boundary stress tensors. We show
that for small entangling intervals, the entanglement entropy obeys the first
law of thermodynamics, as conjectured recently. The saturation of the EE in the
field theory is shown to follow from a version of quantum ergodicity; the
derivation indicates that it should hold for conformal as well as massive
theories in any number of dimensions.
