In this book, the equilibrium and nonequilibrium properties of continuous phase transitions are studied in various systems,
with a special emphasis on understanding how well-established universal traits at equilibrium may be extended into the dynamic
realm, going beyond the paradigmatic Kibble-Zurek mechanism of defect formation. This book reports on the existence of a quantum
phase transition in a system comprising just a single spin and a bosonic mode (the quantum Rabi model). Though critical phenomena
are inherent to many-body physics, the author demonstrates that this small and ostensibly simple system allows us to explore
the rich phenomenology of phase transitions, both in- and out-of-equilibrium. Moreover, the universal traits of this quantum
phase transition may be realized in a single trapped-ion experiment, thus avoiding the need to scale up the number of constituents.
In this system, the phase transition takes place in a suitable limit of system parameters rather than in the conventional
thermodynamic limit - a novel notion that the author and his collaborators have dubbed the finite-component system phase transition.
As such, the results gathered in this book will open promising new avenues in our understanding and exploration of quantum