Thermodynamics is one of the founding scientific pillars that has helped us better understand heat engines, biology, ecosystems, and even black holes. While it fundamentally describes large systems... Show moreThermodynamics is one of the founding scientific pillars that has helped us better understand heat engines, biology, ecosystems, and even black holes. While it fundamentally describes large systems by examining the bulk behavior of their constituents, it is anchored in the statistical equivalence of equilibrium configurations of a formally infinite number of microscopic constituents. A question of its validity arises when one scales down to small quantum systems. Here, we have derived dynamic non-equilibrium relations that surprisingly resemble the classical thermodynamics laws, with a mix of quantum features that encode the dynamics of quantum information. Understanding the relation between the out-of-equilibrium dynamics of finite-size quantum systems and their initial thermodynamic state might have been a purely academic exercise fifteen years ago. But now, thanks to ultra-cold atomic quantum simulators and progress in quantum computers, the thermodynamics of finite-size quantum systems has practical implications too. The findings of this thesis contribute to understanding quantum many-body systems, particularly in the context of entanglement, non-equilibrium dynamics, thermalization, and charge transport. Show less
In this thesis, we examine various systems through the lens of several numerical methods. We delve into questions concerning thermalization in closed unitary systems, lattice gauge theories, and... Show moreIn this thesis, we examine various systems through the lens of several numerical methods. We delve into questions concerning thermalization in closed unitary systems, lattice gauge theories, and the intriguing properties of deep neural network phase spaces. Leveraging modern advancements in both software and hardware, we scrutinize these systems in greater detail, accessing previously unreachable regimes. Show less
