Tightening Time-Energy Uncertainty Relations

The uncertainty principle is a cornerstone of modern physics, and its implications have a fundamental impact on theoretical and applied quantum mechanics. The aim of this thesis is to study and apply the uncertainty relations between time and energy, which are interpreted operationally as the speed limit of quantum evolution. A geometric approach is used to derive improved bounds for the evolution of isolated and open systems and obtain a constructive approach for efficient and fast quantum driving. These results are applied to set the limits for the rate of information transfer and processing, and the power of nanomachines.