From simple particle models to PDE dynamics
Seminar Room 1, Newton Institute
AbstractOne often aims to describe systems out of equilibrium by the governing energy E and entropy S, as well as the corresponding evolution laws for E and S. How can we derive these ingredients of the macroscopic evolution from particle models? In recent years, a dynamic scale-bridging approach has been developed and applied to a number of problems; large deviation theory plays an important role. The talk will present some of these results, focussing on the derivation of the Wasserstein-entropy formulation of diffusion and the Vlasov-Fokker-Planck equation as a system driven by energy and entropy. Time permitting, an approach of deriving stochastic equations mimicking the fluctuations in underlying mesoscopic models will be sketched. This is joint work with Hong Duong, Rob Jack and Mark. A. Peletier.
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