Celebratio Mathematica — Varadhan

Varadhan's work on hydrodynamical limits

Works connected to Leif Arkeryd

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S. R. S. Varadhan: “Entropy methods in hydrodynamic scaling,” pp. 112–145 in Nonequilibrium problems in many-particle systems (Montecatini, Italy, June 15–27, 1992). Edited by L. Arkeryd. Lecture Notes in Mathematics 1551. Springer (Berlin), 1993. MR 1296260 Zbl 0791.60098 incollection

The problem of transition from a microscopic description of a system with a large number of components to the description of a suitably scaled version of the same system by a few macroscopic parameters arises often and is physically natural. However the mathematical justification of such a simplified description is considerably more difficult. The purpose of these lectures is to consider several such models and develop some techniques that can be used for a rigorous study of these models. Our main tool will be entropy and its production. Since entropy production is associated with the existence of stochastic noise in the system we will consider mainly systems with noisy evolution.