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Explore the historical development and recent advances in soliton gas theory through this comprehensive 2-hour lecture delivered at the International Centre for Theoretical Sciences. Delve into the fundamental concepts of soliton gases, examining their evolution from early theoretical foundations to cutting-edge research applications in nonequilibrium statistical physics. Learn how soliton gases connect to broader themes in hydrodynamics, fluctuations, and noise across quantum and classical systems, with particular emphasis on their role in understanding ballistic transport and thermodynamic fluctuations. Discover the mathematical frameworks underlying soliton gas dynamics and their applications to integrable systems, while gaining insights into how these concepts bridge classical nonlinear physics with modern quantum many-body theory. Examine the connections between soliton gases and Generalized Hydrodynamics (GHD), exploring how these theoretical tools contribute to our understanding of thermalization, transport phenomena, and nonequilibrium dynamics in both classical and quantum contexts.
