How do time-dependent entanglement dynamics provide insights into the thermalization and non-equilibrium behavior of quantum systems?

Time-dependent entanglement dynamics study how entanglement evolves in quantum systems out of equilibrium, providing insights into thermalization processes and the emergence of statistical mechanics from quantum mechanics. By analyzing how entanglement spreads and equilibrates, researchers can distinguish between integrable systems, which exhibit slower entanglement growth, and chaotic systems, where entanglement rapidly increases. These studies help understand the mechanisms behind thermalization, the role of conserved quantities, and phenomena like many-body localization, where entanglement dynamics are key to describing non-equilibrium behavior.