From Particle Systems to Partial Differential Equations : Particle Systems and PDEs Braga Portugal December 2012 Mini Course: Fluid dynamic Limits of the Kinetic theory of gases : F. Golse Short Papers: Stationary quasivariational inequalities with gradient constraint and nonhomogeneous boundary conditions: A. Azevedo F. Miranda and L. Santos Shocks and antishocks in the ASEP conditioned on a low current: V. Belitsky and G.M. Schütz Superdiffusion of energy in Hamiltonian systems perturbed by a conservative noise: C. Bernardin Equilibrium fluctuations of additive functionals of zero range models: C. Bernardin P. Gonçalves and S. Sethuraman A survey on Bogoliubov generating functionals for interacting particle systems in the continuum: D.L. Finkelshtein and M. João Oliveira Interacting particle systems: hydrodynamic limit versus high density limit: T. Franco Slowed exclusion process: hydrodynamics fluctuations and phase transitions: T. Franco P. Gonçalves and A. Neumann Exclusion and Zero range in the rarefaction fan: P. Gonçalves Microscopic derivation of an isothermal thermodynamic transformation: S. Olla Unique continuation property for the Benjamin equation: M. Panthee On the kinetic systems for simple reacting spheres: modeling and linearized equations: F. Carvalho J. Polewczak and A. Jacinta Soares Hydrodynamic Limit for the Velocity flip Model: M. Simon Large number asymptotics for two component systems with self consistent coupling: V. Ricci On a stochastic coupled system of reaction diffusion of nonlocal type: E.A. Coayla Terán J. Ferreira P.M.D. de Magalhães and H. B. de Oliveira This book presents the proceedings of the international conference Particle Systems and Partial Differential Equations I which took place at the Centre of Mathematics of the University of Minho Braga Portugal from the 5th to the 7th of December 2012. The purpose of the conference was to bring together world leaders to discuss their topics of expertise and to present some of their latest research developments in those fields. Among the participants were researchers in probability partial differential equations and kinetics theory. The aim of the meeting was to present to a varied public the subject of interacting particle systems its motivation from the viewpoint of physics and its relation with partial differential equations or kinetics theory and to stimulate discussions and possibly new collaborations among researchers with different backgrounds. The book contains lecture notes written by François Golse on the derivation of hydrodynamic equations (compressible and incompressible Euler and Navier Stokes) from the Boltzmann equation and several short papers written by some of the participants in the conference. Among the topics covered by the short papers are hydrodynamic limits; fluctuations; phase transitions; motions of shocks and antishocks in exclusion processes; large number asymptotics for systems with self consistent coupling; quasi variational inequalities; unique continuation properties for PDEs and others. The book will benefit probabilists analysts and mathematicians who are interested in statistical physics stochastic processes partial differential equations and kinetics theory along with physicists