This book presents the lecture notes and articles from the workshop on hydrodynamic limits held at The Fields Institute (Toronto). The first part of the book contains the notes from the mini-course given by Professor S. R. S. Varadhan. The second part contains research articles reviewing the diverse progress in the study of hydrodynamic limits and related areas. This book offers a comprehensive introduction to the theory and its techniques, including entropy and relative entropy methods, large deviation estimates, and techniques in non gradient systems. This book, especially the lectures of Part I, could be used as a text for an advanced graduate course in hydrodynamic limits and interacting particle systems.
Part 1: Lectures on hydrodynamic scaling by S. R. S. Varadhan Part 2: On a 1-d granular media immersed in a fluid by J. A. Carrillo A class of cellular automata equivalent to deterministic particle systems by H. Fuks Recent results on the Ginzburg-Landau $\nabla\phi$ interface model by T. Funaki Large scale behavior of a system of interacting diffusions by I. Grigorescu Stellar dynamics and plasma physics with corrected potentials: Vlasov, Manev, Boltzmann, Smoluchowski by R. Illner Free boundary problem and hydrodynamic limit by J. Quastel A variational coupling for a totally asymmetric exclusion process with long jumps but no passing by T. Seppalainen Quantum mechanics, linear Boltzmann equation and renormalization by H.-T. Yau.