Information-theoretic equilibration: the appearance of irreversibility under complex quantum dynamics

TL;DR

This paper proposes an information-theoretic mechanism explaining how irreversibility emerges in isolated quantum systems with complex dynamics, without relying on decoherence or coarse-graining, supported by numerical and theoretical evidence.

Contribution

It introduces a novel equilibration mechanism based on information constraints, demonstrating irreversibility as a typical phenomenon in complex quantum systems without decoherence.

Findings

Irreversibility emerges under complex quantum dynamics with information constraints.

The mechanism is typical under the random-matrix conjecture for complex systems.

Numerical simulations support the theoretical predictions.

Abstract

The question of how irreversibility can emerge as a generic phenomena when the underlying mechanical theory is reversible has been a long-standing fundamental problem for both classical and quantum mechanics. We describe a mechanism for the appearance of irreversibility that applies to coherent, isolated systems in a pure quantum state. This equilibration mechanism requires only an assumption of sufficiently complex internal dynamics and natural information-theoretic constraints arising from the infeasibility of collecting an astronomical amount of measurement data. Remarkably, we are able to prove that irreversibility can be understood as typical without assuming decoherence or restricting to coarse-grained observables, and hence occurs under distinct conditions and time-scales than those implied by the usual decoherence point of view. We illustrate the effect numerically in several model systems and prove that the effect is typical under the standard random-matrix conjecture for complex quantum systems.