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Classical physics provides an arrow of time in the form of the second law ofthermodynamics. But a clear picture of the quantum origin of the arrow of timehas been lacking so far. In this letter, we show that an arrow of time arisesin quantum chaotic systems. We show that, for an isolated quantum system whichis also chaotic, the change in entropy is non-negative when the system isperturbed. We show that this gives rise to a new profound constraint on theoff-diagonal terms in eigenstate thermalization hypothesis (ETH) statement. Incase of an integrable system, second law does not hold true because the systemdoes not thermalize to a generalized Gibbs ensemble after a finiteperturbation.

Quantum chaos and the arrow of time