  A global quench is an interesting setting where we can study thermalization
of subsystems in a pure state. We investigate entanglement entropy (EE) growth
in global quenches in holographic field theories and relate some of its aspects
to quantities characterizing chaos. More specifically we obtain four key
results:
  1. We prove holographic bounds on the entanglement velocity $v_E$ and the
butterfly effect speed $v_B$ that arises in the study of chaos.
  2. We obtain the EE as a function of time for large spherical entangling
surfaces analytically. We show that the EE is insensitive to the details of the
initial state or quench protocol.
  3. In a thermofield double state we determine analytically the two-sided
mutual information between two large concentric spheres separated in time.
  4. We derive a bound on the rate of growth of EE for arbitrary shapes, and
develop an expansion for EE at early times.
  In a companion paper arXiv:1608.05101, we put these results in the broader
context of EE growth in chaotic systems: we relate EE growth to the chaotic
spreading of operators, derive bounds on EE at a given time, and compare the
holographic results to spin chain numerics and toy models. In this paper, we
perform holographic calculations that provide the basis of arguments presented
in that paper.
