Quantum thermodynamics and information

Nanoscale devices are ubiquitous in performing tasks such as converting energy into useful work or functioning as measurement devices delivering information about a process or small system. This lecture offers an introduction to the field of quantum thermodynamics and information, which explores how thermodynamic and statistical concepts, such as heat, work, temperature, and information, are applied to nanotechnological devices, where fluctuations and probabilistic behavior are intrinsic.

The course will begin by revisiting the laws of thermodynamics for quantum systems interacting with larger environments, and will define standard thermodynamic properties such as heat, energy, entropy, free energy, and more. These concepts will then be applied to quantum thermal machines operating between two (or more) heat reservoirs, such as quantum dot heat engines or absorption refrigerators (comprising collections of qubits) for qubit cooling, whose dynamics will be described using Markovian master equations. Performance metrics for these quantum machines, including power output, efficiency in converting heat to useful work, and work-to-cooling power conversion, will be discussed.

Since nano-engines are subject to particle and energy fluctuations due to their small size, the lecture will further introduce the concept of stochastic thermodynamics, using a description based on single trajectories of the system's evolution. Energy, entropy, and their fluctuations along these stochastic trajectories will be explored. Key ideas such as local detailed balance and fluctuation relations, like the thermodynamic uncertainty relation as bounds on heat production by fluctuations, will also be covered.

Measurement and information are not only essential resources for controlling the thermodynamics of nanoscale devices but also for quantum computing. This lecture will introduce the general principles of measurement, information, and feedback from a thermodynamic perspective using the example of the Szilard engine. Concepts such as Landauer's principle of information erasure, the cost of measurement, and the role of information as a physical quantity in the second law of thermodynamics will be discussed. The influence of information and measurement on the previously introduced thermodynamic fluctuation relations will also be examined. Additionally, an introduction to general measurement theory will be provided, including the concept of Positive Operator-Valued Measures (POVMs) to describe quantum measurement processes.

The course concludes with an overview of full counting statistics, introducing the concept of counting fields as a method for quantifying the statistical properties of energy and particle exchanges in quantum systems operating between two or more thermal environments.

Methods

The course will run over a period of 8 weeks, with two sessions per week. After every two lecture sessions, an exercise session will be held. A total of three major exercise sheets will be distributed during the course. For each exercise sheet, there will be an exercise session to introduce into the bigger problem set followed by a session where the solutions are discussed. Participants will be assessed based on a final oral exam. The course will be conducted in person but will also be recorded to enable remote participation, particularly for students from other Nordic universities.

Time: Mondays (10-12h), Tuesdays (10-12h), Fridays (15-17h, Exercise)
Room: MC2 Kollektorn / possibility to join remotely (hybrid lecture)

Contact course administrator

Henning Kirchberg, Juliette Monsel, Janine Splettstoesser