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Explore the Eigenstate Thermalization Hypothesis in this comprehensive 2-hour lecture delivered at the International Centre for Theoretical Sciences as part of the "Hydrodynamics, Fluctuations, and Noise in quantum and classical systems" program. Delve into one of the fundamental concepts that has revolutionized our understanding of thermalization in isolated quantum systems over the past two decades. Learn how this hypothesis provides crucial insights into how quantum many-body systems reach thermal equilibrium, connecting microscopic quantum mechanics to macroscopic thermodynamics. Examine the theoretical framework that explains why isolated quantum systems can exhibit thermal behavior despite their unitary evolution, and understand its implications for quantum chaos, transport phenomena, and the emergence of classical statistical mechanics from quantum foundations. Discover how this concept relates to broader developments in nonequilibrium quantum physics, including Generalized Gibbs Ensembles, many-body localization, and dynamical phase transitions. Gain insights into the connections between quantum thermalization and classical statistical physics, as well as the role of eigenstate properties in determining thermodynamic behavior. This lecture forms part of an interdisciplinary workshop bringing together perspectives from classical statistical physics, quantum many-body theory, and string theory to advance understanding of nonequilibrium hydrodynamics across different physical contexts.
