Abstract: In the study of out-of-equilibrium many-body quantum systems, growing attention has been given to understanding how symmetries evolve over time under unitary dynamics. Key questions include whether symmetries are dynamically restored in local subsystems and how the timescales involved depend on the initial states and the dynamics of the system. In this talk, we introduce the entanglement asymmetry as a versatile and practical tool for probing symmetry breaking and restoration in extended quantum systems. Specifically, we investigate the evolution of a symmetry that is initially preserved but subsequently broken by random unitary dynamics. At late times, the system's behavior matches that of a random state of qubits, which serves as an effective model for a black hole. Finally, we will show that, in setups where the symmetry is restored, the entanglement asymmetry neatly detects an unexpected quantum version of the Mpemba effect.