Communications in Mathematical Sciences

Volume 9 (2011)

Number 2

Kramers’ formula for chemical reactions in the context of Wasserstein gradient flows

Pages: 623 – 635

(Fast Communication)

DOI: http://dx.doi.org/10.4310/CMS.2011.v9.n2.a15

Authors

Michael Herrmann (Oxford Centre for Nonlinear PDE (OxPDE), University of Oxford, United Kingdom)

Barbara Niethammer (Oxford Centre for Nonlinear PDE (OxPDE), University of Oxford, United Kingdom)

Abstract

We derive Kramers’ formula as singular limit of the Fokker–Planck equation with double-well potential. The convergence proof is based on the Rayleigh principle of the underlying Wasserstein gradient structure and complements a recent result by Peletier, Savaré and Veneroni.

Keywords

Kramers’ formula, Fokker-Planck equation, Wasserstein gradient flow, Rayleigh principle

2010 Mathematics Subject Classification

35Q84, 49S05, 80A30

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