Macroscopic limits of microscopic systems - C. BOLDRIGHINI (Rendiconti di Matematica e delle Sue Applicazioni, 1996)
The present paper is meant as an introduction for the mathematically educated reader to problems of macroscopic limits of microscopic systems, and to the derivation of PDE's which describe the evolution of continuous media. The hydrodynamic, mean field and kinetic limits are considered for various models, which are chosen as simple as possible, the aim being of conveying the main ideas which led in recent years to the first steps in rigorous nonequilibrium statistical mechanics. The paper is self contained, as far as possible, in the sense that the mathematical notions that are needed are as a rule introduced in the text.