The ERC Starting Grant project "ODYSSEY, focused on advancing the theoretical understanding of thermodynamics in complex quantum systems. Specifically, the research addressed how quantum systems connected to multiple heat baths behave under the combined influence of inter-particle interactions, disorder, and non-equilibrium driving forces. The overarching aim was to uncover the fundamental principles governing thermal transport and energy conversion at the nanoscale. The project tackled the challenge of describing energy flow and thermodynamic behavior in strongly interacting quantum systems beyond conventional theoretical methods. Current models often broke down in regimes with strong interactions, high levels of disorder, or far-from-equilibrium conditions, leaving significant gaps in understanding. A core issue was determining how microscopic properties like inter-particle interactions and impurities influenced macroscopic thermodynamic behavior, including energy efficiency, thermal conductivity, and heat-to-work conversion. The study of thermodynamics at the nanoscale was crucial for developing next-generation technologies, particularly in the context of energy efficiency and quantum information processing. As society faced increasing demands for sustainable energy and efficient devices, understanding the thermodynamic principles at microscopic scales became essential. Quantum technologies, such as quantum computers and sensors, relied on precise control of non-equilibrium processes, making it vital to explore how energy dissipated and flowed in these systems. Insights gained from this research enabled the design of devices with enhanced thermal functionality, contributing to a more sustainable technological future. The primary objective of the project was to build a comprehensive theoretical framework for non-equilibrium quantum thermodynamics that accounted for the interplay between interactions, disorder, and quantum coherence. Develop numerical and analytical models that extended beyond the limits of linear response theory. Investigate thermal transport in non-ergodic and disordered quantum systems, where conventional assumptions about thermalization might fail. Explore how imperfections such as impurities could be harnessed to optimize thermal performance rather than degrade it and Identify fundamental limits and possibilities for energy-efficient quantum devices by studying steady-state and transient heat flows. By addressing these objectives, the project contributed to foundational research with direct relevance to the development of more efficient energy technologies and the next generation of quantum devices. Through innovative theoretical approaches, the project advanced the understanding of how quantum mechanical principles could be leveraged for practical technological applications, paving the way toward a deeper grasp of energy management at the quantum level.
