Quantum chaos and the arrow of time

TL;DR

This paper demonstrates that quantum chaotic many-body systems inherently exhibit the thermodynamic arrow of time in the thermodynamic limit, supported by theoretical arguments and numerical verification, and introduces new ETH constraints.

Contribution

It establishes the presence of the thermodynamic arrow of time in quantum chaotic systems and introduces ETH-monotonicity constraints that go beyond entropic considerations.

Findings

Quantum chaotic systems exhibit the thermodynamic arrow of time.

Numerical calculations support the theoretical predictions.

New ETH constraints, called ETH-monotonicity, are identified.

Abstract

We show that quantum chaotic many-body systems possess the thermodynamic arrow of time in the thermodynamic limit. Berry's conjecture in quantum chaotic systems and equivalence of ensembles imply the Kelvin statement of the second law of thermodynamics at leading order in perturbation theory. We verify this result using numerical calculations. We also show that this gives rise to new constraints on the off-diagonal terms in eigenstate thermalization hypothesis (ETH) statement. We call the new constraints collectively as ETH-monotonicity. These constraints arise because pure entropic consideration is not enough for the emergence of the thermodynamic arrow of time.