Fluctuations and Geometry in Quantum Thermodynamics

Abstract

Understanding thermodynamics at the quantum scale is a central challenge in modern physics. Thermodynamic concepts were originally formulated for macroscopic systems, where fluctuations are negligible and quantum features are effectively washed out. For quantum systems operating far from equilibrium, these assumptions break down, motivating the development of nonequilibrium quantum thermodynamics. At the same time, engineered quantum platforms, ranging from superconducting circuits and cavity QED to mesoscopic conductors, now provide experimentally accessible settings in which this theoretical framework can be systematically tested and, increasingly, applied to practical tasks. This thesis addresses a broad range of problems in the nonequilibrium thermodynamics of open quantum systems, organised around two central themes: fluctuations and geometry. Our work spans measurement-induced effects, stochastic dynamics beyond the Markovian weak-coupling regime, information-geometric aspects, and dissipative critical phenomena, and accordingly employs a wide array of theoretical tools. Specifically, we propose a model of measurement-boosted quantum transport within the framework of repeated interactions, and demonstrate that measurement backaction can enhance both the performance and stability of quantum heat engines. We then introduce a method for directly sampling the time- and energy resolved statistics of thermodynamic quantities in strongly coupled, driven open quantum systems, by combining Markovian embeddings with quantum-jump trajectory unravellings. Using tools from information geometry, we relate the temporal quantum Fisher information to entropic fluxes in open quantum systems and develop a geometric description of the thermodynamic cost associated with slow transitions between nonequilibrium steady states. This approach yields general bounds on excess entropy flux and nonadiabatic entropy production and, owing to their geometric origin, naturally suggests dissipation-minimising protocols based on geodesic paths. Finally, we apply thermodynamic geometry to dissipative quantum phase transitions, revealing dynamical universality in the nonadiabatic entropy production under finite-speed driving. These results constitute a far-from-equilibrium analogue of the celebrated Kibble-Zurek mechanism.