Thermodynamics of Speed and Efficiency with Quantum Feedback

Introduction

Rapid thermodynamic processes inevitably generate irreversible dissipation, creating a classic trade‑off between how fast a transformation can be performed and the energetic cost incurred. In the quantum realm, continuous monitoring and feedback add layers of complexity: measurement back‑action, stochastic jumps, and informational contributions all intertwine with the system’s dynamics. The recent preprint Thermodynamics of Speed and Efficiency with Quantum Feedback (Liu, Honma, Bao, Vu, arXiv:2611.08564) tackles this challenge head‑on. By deriving a finite‑time current‑dissipation relation for open quantum systems subject to jump‑type feedback, the authors provide a quantitative foundation for fast, low‑dissipation quantum thermodynamics.

Finite‑time current‑dissipation relation

The core result is a relation that links the average particle (or energy) current flowing through a continuously monitored quantum system to the total entropy production over a finite observation window. Unlike traditional steady‑state fluctuation theorems, this relation explicitly incorporates the stochastic nature of quantum jumps and the deterministic control actions applied after each detection event (the feedback). The authors show that the feedback modifies both the dynamical contribution (through altered transition rates) and the informational contribution (through the entropy associated with measurement outcomes). This dual influence is captured in a compact expression that serves as a starting point for subsequent bounds.

Quantum speed limit and power‑efficiency trade‑off

From the current‑dissipation relation, the paper derives two key performance limits for stationary information engines:

1. Quantum speed limit (QSL). The QSL quantifies the minimal time required to drive the system between two states under continuous monitoring and feedback. It depends on the average current, the dissipation, and the information gained from measurements. The bound reveals that feedback can tighten the QSL, enabling faster state transformations without proportionally increasing entropy production.
2. Power‑efficiency trade‑off. For engines that extract work from information (e.g., Maxwell‑demon‑type devices), the authors establish a relation between output power, thermodynamic efficiency, and the feedback‑induced informational entropy flow. The trade‑off shows that, at finite power, the efficiency can approach unity when the system size grows large, highlighting a route to near‑optimal information‑to‑work conversion.

These results unify dynamical and informational aspects of quantum thermodynamics, offering a clearer picture of how feedback reshapes fundamental limits.

Illustrative applications

The authors demonstrate the utility of their framework with two concrete examples:

• Finite‑time information erasure. By applying optimal feedback during the erasure of a qubit’s state, the protocol reaches the generalized Landauer bound within a finite duration, illustrating that the minimal thermodynamic cost can be achieved without requiring quasistatic operations.
• Collective information engine. In a many‑body setting, a collective engine operating under feedback can attain unit information efficiency at finite power as the number of constituents becomes large. This scaling behavior underscores the potential of feedback‑enhanced designs for scalable quantum technologies.

Both cases emphasize that feedback not only supplies information but also directly alters the system’s dynamics, thereby reducing dissipation while maintaining speed.

Practical outlook

The finite‑time current‑dissipation relation and its derived bounds provide a versatile toolkit for designing quantum thermodynamic protocols. Researchers developing quantum computers, nanoscale heat engines, or measurement‑based control schemes can use these results to benchmark performance, optimize feedback strategies, and assess the thermodynamic cost of rapid operations. Moreover, the framework invites experimental verification in platforms such as superconducting circuits, trapped ions, or optomechanical systems where continuous monitoring and real‑time feedback are already feasible.

--- The paper offers a rigorous, experimentally relevant foundation for fast, low‑dissipation quantum thermodynamics, highlighting how feedback can simultaneously accelerate state changes and improve energetic efficiency.