Quantum work statistics of controlled evolutions

TL;DR

This paper investigates how quantum work statistics, especially the Shannon entropy of work distributions, can characterize controlled quantum evolutions and their complexity, revealing insights into non-equilibrium dynamics and control requirements.

Contribution

It introduces the use of work distribution entropy as a tool to analyze controlled quantum dynamics and links it to the Kibble-Zurek mechanism and control complexity in many-body systems.

Findings

Work distribution entropy scales with the Kibble-Zurek mechanism in Landau-Zener models.

Entropy serves as a summary statistic for control field complexity.

Thermodynamics provides insights into non-equilibrium quantum dynamics.

Abstract

We use the quantum work statistics to characterize the controlled dynamics governed by a counterdiabatic driving field. Focusing on the Shannon entropy of the work probability distribution, $P(W)$, we demonstrate that the thermodynamics of a controlled evolution serves as an insightful tool for studying the non-equilibrium dynamics of complex quantum systems. In particular, we show that the entropy of $P(W)$ recovers the expected scaling according to the Kibble-Zurek mechanism for the Landau-Zener model. Furthermore, we propose that the entropy of the work distribution provides a useful summary statistic for characterizing the need and complexity of the control fields for many-body systems.