  Classical arguments for thermalization of isolated systems do not apply in a
straightforward way to the quantum case. Recently, there has been interest in
diagnostics of quantum chaos in many- body systems. In the classical case,
chaos is a popular explanation for the legitimacy of the methods of statistical
physics. In this work, we relate a previously proposed criteria of quantum
chaos in the unitary time evolution operator to the entanglement entropy growth
for a far-from-equilibrium initial pure state. By mapping the unitary time
evolution operator to a doubled state, chaos can be characterized by
suppression of mutual information between subsystems of the past and that of
the future. We show that when this mutual information is small, a typical
unentangled initial state will evolve to a highly entangled final state. Our
result provides a more concrete connection between quantum chaos and
thermalization in many-body systems.
