Explore quantum phenomena through two specialized lectures from the II School on Emergent Phenomena in Non-Equilibrium Quantum Many-Body Systems. Learn about cold atoms in bad cavities as an ideal experimental platform for studying quantum phenomena with Felipe Reyes Osorio from the University of Delaware, Colombia, who demonstrates how these systems provide perfect conditions for quantum research. Discover the accuracy of time-dependent Generalized Gibbs Ensembles (GGE) with Gianni Aupetit-Diallo from SISSA, Italy, who examines the precision and reliability of this theoretical framework in non-equilibrium quantum systems. Gain insights into cutting-edge research methodologies in quantum many-body physics, understand the experimental advantages of cavity-atom systems, and explore advanced theoretical approaches to describing non-equilibrium quantum states through these complementary perspectives on emergent quantum phenomena.