Physics

Toronto Team Maps Entropy Production in Driven Quantum Subsystems

Avatar of Ivy Delaney
October 31, 2026 by Ivy Delaney

Reservoirs represent an important area of study. Local density operators function as functionals of constraint variables which serve as thermodynamic forces satisfying a set of equations of motion. The evolution of average internal energy within the quantum subsystem, potentially subject to external autonomous driving performing work on it, is a primary focus. Entropy production within the system also receives sharp attention.

Nonequilibrium statistical thermodynamics pertaining to both the quantum subsystem coupled to reservoirs and that for isolated subsystems and reservoirs are discussed. When coupling the subsystem with large quantum reservoirs, impacts from the quantum subsystem upon those reservoirs become quantifiable via boundary conditions.

Exact Quantum Averages Enable Reservoir-Aware Energy Evolution Calculations

Jeremy Schofield and Raymond Kapral (University of Toronto) have developed a statistical mechanical framework yielding exact expressions for quantum system averages, a feat previously limited to approximations. The new formulation allows calculation of internal energy evolution equations that capture reservoir effects via derived boundary conditions, something earlier methods could not accurately quantify regarding subsystem impact on large reservoirs. Local density operators constructed by maximising entropy subject to constraints on observable averages provide insights into both driven systems and their surrounding environments, crucial information for nanoscale device modelling.

A small quantum system’s impact on large reservoirs can now be calculated through newly derived boundary conditions inaccessible with previous techniques. Detailed analysis of a specific work protocol established relationships between external driving forces and changes in internal energy, regardless of whether processes are reversible or irreversible. While effective with two thermal reservoirs at differing temperatures, extending these calculations to larger or more complex arrangements presents an immediate challenge; computational efficiency beyond this case remains unclear.

Precise energy flow analysis enables study of complex nanoscale systems

An exact method for calculating average properties like internal energy and entropy production within small quantum devices is offered by this new framework, understanding energy flow becomes increasingly important as they shrink further. The approach utilizes ‘local density operators’ describing parts of the system, providing a precise calculation method while acknowledging that scaling these computations to intricate quantum setups will be computationally demanding, yet doesn’t diminish its significance.

Scientists at University of Liège believe their work will unlock more efficient designs for future nanoscale technologies here, particularly because it also derives boundary conditions quantifying subsystem impact on surrounding reservoirs, something previous methods struggled with and which is vital in modelling nanoscale devices.

This statistical mechanical framework describes open quantum systems, small components interacting with larger ‘reservoirs’, by calculating average properties exactly rather than through approximation; observable averages subject to certain constraints define the system. It defines the system using observable averages subject to certain constraints, a significant advancement over prior approximations. The ability to precisely model energy exchange between these subsystems and reservoirs promises a deeper understanding of complex nanoscale phenomena.

This research developed a new method for calculating average internal energy and entropy production in small quantum systems connected to external environments, called “reservoirs”. This approach calculates these values exactly using local density operators, offering improved precision compared to previous techniques that relied on approximations. Importantly, it also establishes boundary conditions describing how the quantum system influences its surrounding reservoirs, which is crucial for accurate modeling at the nanoscale. While currently demonstrated with two heat reservoirs with different temperatures, extending this framework to more complicated arrangements remains computationally challenging.

👉 More information
🗞 Nonequilibrium statistical thermodynamics of a small quantum system coupled to quantum reservoirs
✍️ Jeremy Schofield and Raymond Kapral (University of Toronto)
🧠 ArXiv: https://arxiv.org/abs/2610.39973

More like this
PhysicsResearchers Measure Topological Shifts Using Particle Count
Quantum Research NewsJoint Quantum Institute at University of Maryland builds compact frequency comb
PhysicsMilano Team Speeds up Quantum Simulations with New Method
Quantum Research NewsImaging model links quantum states to data analysis
Stay current

See today’s quantum computing news on Quantum Zeitgeist for the latest breakthroughs in qubits, hardware, algorithms, and industry deals.

Tags:
Avatar of Ivy Delaney

Ivy Delaney

Ivy Delaney has been working with neural networks and machine learning since the mid-nineties, back when a couple of hidden layers and a long afternoon of training counted as ambitious. She has watched the field go from academic curiosity to the thing quietly running underneath everything, and she brings that long view to quantum computing. For Quantum Zeitgeist she covers the ground where the two fields meet. That means quantum machine learning and the variational algorithms it leans on, and it also means the less glamorous but more interesting story of classical machine learning already doing real work inside quantum machines, decoding error-correcting codes, calibrating noisy hardware and learning the error models that simulators depend on. She writes about the hardware those algorithms have to run on too, and about the post-quantum cryptography scramble that the same hardware has set off. Her stories typically start with the paper, whether that is peer-reviewed work, conference proceedings or an arXiv preprint, with the source linked so you can hold a claim up against the research it came from. She is unimpressed by benchmarks that will not say what they beat, and by demonstrations that only work in the press release.

Latest Posts by Ivy Delaney: