Work fluctuations in quantum systems are accurately bounded even when these systems constantly interact with their environment. A new thermodynamic uncertainty relation quantifies these fluctuations within open quantum systems undergoing time-dependent changes and measured using projective energy measurements. The development allows computation of lower bounds on the variance of work performed by such systems, relying on combining information about how quickly the system responds to change with its entropy production.

New limits have been defined on variations observed when measuring energy changes in small quantum systems affected by their surroundings. This refines existing thermodynamic uncertainty relations to account for scenarios involving ongoing energy loss during measurements, improving upon previous theoretical models. Quantifying these fluctuations is key for optimising how energy transfers within open quantum systems operate at tiny scales; this applies across multiple industries including materials science and nanotechnology.

New limits exist on how accurately work fluctuations can be measured in small, dynamic quantum systems. Understanding these variations is vital as energy transfer operates differently at tiny scales, having implications across materials science and nanotechnology.

The team focused on ‘open’ quantum systems, those interacting with their environment causing a loss of energy or information akin to friction slowing down movement, and used projective energy measurements, essentially sorting the system into specific energy states before discarding everything else, to quantify changes during time-dependent processes. These findings refine existing theoretical models by accounting for ongoing energy loss during measurement; researchers now seek to understand whether tighter bounds depend on both the driving protocol and switching timescales involved.

Reduced Quantum Work Variance via Precision-Energy Cost Relationships

Variances in quantum work are now bounded to below 2/E, specifically achieving values below 2/E where E represents dimensionless entropy production, according to scientists at Department of Physics, Myongji University, This improvement surpasses existing thermodynamic uncertainty relations which previously lacked precise quantification for open quantum systems undergoing both dissipation and projective energy measurements, a common scenario in nanoscale devices. Establishing this lower bound on work variance utilises Fisher information and dynamical activity alongside entropy production, unlocking more accurate modelling of energy transfer processes.

A direct link between measurement precision and inherent energetic costs within these changing quantum systems has been revealed; tighter bounds become achievable depending upon process characteristics and timescale. Validating the results involved applying the derived uncertainty relation to two-level systems driven by square-wave and sinusoidal protocols. Simulations showed that rapidly switched protocols, those completed within very short intervals, saw limits determined by dynamical activity becoming dominant, indicating greater energetic cost linked to faster changes in the system’s Hamiltonian.

Conversely, slower transitions favoured limits dictated by entropy production, highlighting dissipation as a primary factor limiting work measurement precision under such conditions. Gallavotti, Cohen symmetry exists within accumulated work statistics, underpinning established fluctuation theorems like Crooks and Jarzynski relations which describe probability distributions of energy change.

Establishing energetic limits in simplified systems informs design of advanced nanodevices

Quantifying work fluctuations is important for optimising energy transfer in nanoscale devices spanning materials science to quantum computing; however, this analysis presently applies only to a simple two-level system responding to specific waveforms. Will it hold true with increasing systemic complexity or diminish, this raises an important question regarding its validity across more complex architectures and diverse driving protocols. Nevertheless, establishing a fundamental inequality relating work fluctuations to system characteristics remains valuable for nanoscale engineering applications.

Myongji University’s team has established a new thermodynamic uncertainty relation defining fundamental limits on how accurately work fluctuations can be measured in open quantum systems constantly interacting with their environment and experiencing energy loss similar to friction. The resulting inequality connects the variance of work performed, as a measure of energetic spread, to Fisher information and dynamical activity describing system responsiveness alongside entropy production quantifying disorder.

The researchers demonstrated a thermodynamic uncertainty relation that defines a lower bound on the precision with which work done within an open quantum system can be determined. This finding establishes a connection between unavoidable fluctuations in work and characteristics of the system such as its response to change and the amount of energy lost to dissipation.

Applying this relationship to two-level systems revealed that faster protocols are limited by energetic cost while slower transitions are governed by dissipation during measurement. The authors suggest further investigation is needed to determine if these limits hold true for more complex systems and diverse driving methods.

👉 More information
🗞 Thermodynamic Uncertainty of Work in Time-Dependently Driven Open Quantum Systems
✍️ Chulan Kwon
🧠 ArXiv: https://arxiv.org/abs/2609.17032

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