In this thesis we introduce a new quantity which we call the dynamic fidelity susceptibility (DFS). We show that it is relevant to out-of-equilibrium dynamics in many-particle quantum systems, taking the problem of an impurity in a Bosonic Josephson junction, and the transverse field Ising model, as examples. Both of these systems feature quantum phase transitions in their ground states and understanding the dynamics near such critical points is currently an active area of research. In particular, sweeping a system through a quantum critical point at finite speed leads to non-adiabatic dynamics. A simple theoretical tool for describing such a scenario is the celebrated Kibble-Zurek theory which predicts that the number of excitations is related to the speed of sweep via the phase transition’s critical exponents at equilibrium. Another theoretical tool, useful in describing the static properties of quantum phase transitions, is the fidelity susceptibility. Our DFS generalizes the concept of fidelity susceptibility to nonequilibrium dynamics, reproducing its results in the static limit, whilst also displaying universal scaling properties, akin to those found in Kibble-Zurek theory, in the non-adiabatic regime. Furthermore, we show that the DFS is the same quantity as the time-dependent quantum Fisher information which provides a measure of multi-partite entanglement, as well as being closely related to out-of-time-order correlators (OTOCs). / Thesis / Master of Science (MSc)