  Classical physics possesses an arrow of time in the form of the second law of
thermodynamics. But a clear picture of the quantum origin of the arrow of time
has been lacking so far. In this letter, we show that an arrow of time arises
naturally in quantum chaotic systems. We show that, for an isolated quantum
system which is also chaotic, the change in entropy is non-negative when the
system is perturbed. At leading order in perturbation theory, this result
follows from Berry's conjecture and eigenstate thermalization hypothesis (ETH).
We show that this gives rise to a new profound constraint on the off-diagonal
terms in the ETH statement. In case of an integrable system, the second law
does not hold true because the system does not thermalize to a generalized
Gibbs ensemble after a finite perturbation.
