Introduction

The concept of time has always had a prominent role in any physical theory and in any human attempt to understand reality. One of the main goals of physics is to describe the dynamics of physical systems, that is, to predict their evolution in time. The extent to which this goal can be achieved depends on the amount of complexity that emerges during the evolution. Notably, physical systems with many degrees of freedom are much harder to describe. In quantum mechanics, to this very general observation we have to add the intrinsic indeterminacy that lies at the core of the theory. As a result, characterizing quantum dynamics often becomes a complicated task that cannot be fulfilled completely. Whenever exact solutions are not available, it appears crucial to provide some bounds capable of constraining the dynamics [1].