Nonequilibrium Fluctuations, Martingales, and Information in Quantum Thermodynamics
In the last two decades, thermodynamics has been extended to describe small systems, where the action of environmental noise “blurs” traditional thermodynamic constraints. The second law of thermodynamics is then manifested on a statistical level through the emergence of a set of universal nonequilibrium fluctuation relations. These impose fundamental restrictions on the shape that distributions of thermodynamic quantities such as work, heat or entropy production may take. The underlying structure of fluctuations may be further altered in the presence of quantum effects, like coherence or entanglement, challenging precedent thermodynamic intuition and leading to situations that started to be accessible in the laboratory only very recently.
The understanding of the role of quantumness in thermodynamic fluctuations and their possible applications is one of the major challenges in quantum thermodynamics. This project is in line with this path of research. Using various techniques from stochastic processes, open quantum systems, and quantum measurement theory, the project will be focused on the full development of a quantum Martingale theory for the description of entropy production fluctuations in nonequilibrium processes and their connections to information. This includes the study of quantum effects on extreme fluctuations of thermodynamic quantities as well as situations where stopping (or “gambling”) strategies come into play. The plan is to apply the general theory to setups of fundamental interest, like Maxwell’s demon setups, quantum transport with non-commuting charges, or thermal models for quantum clocks. This may shed new light on some fundamental issues, like the nature of irreversibility and the arrow of time, or the link between information and thermodynamics.