Microscopic Models and Macroscopic Equations

Joel Lebowitz
Rutgers University

The derivation of macroscopic equations, giving a coarse grained description of the microscopic entities making up a system, be they atoms or animals, is one of the central objectives of statistical mechanics. There are in many cases, strong interplays between the different levels of description which are useful for both understanding the microscopic systems and for obtaining solutions of the macroscopic equations. I will discuss several examples where specific microscopic
models lead in some appropriate scaling limits, approximately or rigorously, to macroscopic equations which apply to more general situations than those originally considered. This is a form of universality which makes the subject fascinating.

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