Relaxation of Multitime Statistics in Quantum Systems

Abstract

Equilibrium statistical mechanics provides powerful tools to understand physics at the macroscale. Yet, the question remains how this can be justified based on a microscopic quantum description. Here, we extend the ideas of pure state quantum statistical mechanics, which focus on single time statistics, to show the equilibration of isolated quantum processes. Namely, we show that most multitime observables for sufficiently large times cannot distinguish a nonequilibrium process from an equilibrium one, unless the system is probed for an extremely large number of times or the observable is particularly fine-grained. A corollary of our results is that the size of non-Markovianity and other multitime characteristics of a nonequilibrium process also equilibrate.

arXiv comment7+13 pages, 2+2 figures

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• Operational Metric for Quantum Chaos and the Corresponding Spatiotemporal Entanglement Structure
• Classicality with(out) decoherence: Concepts, relation to Markovianity, and a random matrix theory approach
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• Symmetry Properties of Quantum Dynamical Entropy
• Diagnosing chaos with projected ensembles of process tensors