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Explore the fundamental principles of hydrodynamics and generalized hydrodynamics in this comprehensive lecture delivered at the International Centre for Theoretical Sciences. Delve into the theoretical foundations that underpin both classical and quantum nonequilibrium systems, examining how hydrodynamic principles apply across different physical contexts. Learn about the mathematical frameworks and conceptual tools used to describe fluid-like behavior in many-body systems, including the transition from traditional hydrodynamics to generalized hydrodynamics. Discover how these principles connect classical statistical mechanics with quantum many-body physics, particularly in the context of integrable systems and ballistic transport. Examine the role of conservation laws and their impact on the emergence of hydrodynamic behavior in both equilibrium and nonequilibrium scenarios. Understand the theoretical developments that have bridged classical hard-rod gas theory with quantum systems, revealing universal structures in transport phenomena. Gain insights into how these fundamental principles contribute to our understanding of thermalization, chaos, and transport in isolated quantum systems, while exploring connections to experimental observations in cold-atom systems and other quantum platforms.
