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Entropy and Partial Differential Equations

Entropy and Partial Di erential Equations Lawrence C. Evans Department of Mathematics, UC Berkeley Inspiring Quotations A good many times I have been present at gatherings of people who, by the standards of traditional culture, are thought highly educated and who have with considerable gusto been expressing their incredulity at the illiteracy of scientists. Once or twice I have been provoked and have asked the company how many of them could describe the Second Law of Thermodynamics. The response was cold: it was also negative. Yet I was asking something which is about the scienti c equivalent of: Have you read a work of Shakespeare's?

D. Small noise in dynamical systems 1. Stochastic differential equations 2. Itˆo’s formula, elliptic PDE 3. An exit problem a. Small noise asymptotics b. Perturbations against the flow Appendices: A. Units and constants B. Physical axioms References 4

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