Kramers’ formula for chemical reactions in the context of Wasserstein gradient flows
نویسندگان
چکیده
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 Wasser-stein gradient structure and complements a recent result by Peletier, Savaré and Veneroni.
منابع مشابه
Well-posedness of a parabolic moving-boundary problem in the setting of Wasserstein gradient flows
We develop a gradient-flow framework based on the Wasserstein metric for a parabolic moving-boundary problem that models crystal dissolution and precipitation. In doing so we derive a new weak formulation for this moving-boundary problem and we show that this formulation is well-posed. In addition, we develop a new uniqueness technique based on the framework of gradient flows with respect to th...
متن کاملFirst variation formula in Wasserstein spaces over compact Alexandrov spaces
We extend results proven by the second author ([Oh]) for nonnegatively curved Alexandrov spaces to general compact Alexandrov spacesX with curvature bounded below: the gradient flow of a geodesically convex functional on the quadratic Wasserstein space (P(X),W2) satisfies the evolution variational inequality. Moreover, the gradient flow enjoys uniqueness and contractivity. These results are obt...
متن کاملLecture notes Particle systems, large-deviation and variational approaches to generalised gradient flows
In 1998, Jordan-Kinderleher-Otto [JKO98] proved a remarkable result that the diffusion equation can be seen as a gradient flow of the Boltzmann entropy with respect to the Wasserstein distance. This result has sparked off a large body of research in the field of partial differential equations and others in the last two decades. Many evolution equations have been proved to have a Wasserstein gra...
متن کاملGradient Flows on Wasserstein Spaces over Compact Alexandrov Spaces
We establish the existence of Euclidean tangent cones on Wasserstein spaces over compact Alexandrov spaces of curvature bounded below. By using this Riemannian structure, we formulate and construct gradient flows of functions on such spaces. If the underlying space is a Riemannian manifold of nonnegative sectional curvature, then our gradient flow of the free energy produces a solution of the l...
متن کاملA Smoothed Dual Approach for Variational Wasserstein Problems
Variational problems that involve Wasserstein distances have been recently proposed to summarize and learn from probability measures. Despite being conceptually simple, such problems are computationally challenging because they involve minimizing over quantities (Wasserstein distances) that are themselves hard to compute. We show that the dual formulation of Wasserstein variational problems int...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010