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

TL;DR

This paper derives Kramers' formula for chemical reaction rates as a singular limit of the Fokker-Planck equation with a double-well potential, using Wasserstein gradient flow techniques.

Contribution

It provides a new convergence proof of Kramers' formula based on Wasserstein gradient structures, extending recent theoretical results.

Findings

Kramers' formula derived as a limit of Fokker-Planck equation

Convergence proof utilizes Wasserstein gradient flow principles

Complements existing theoretical frameworks for reaction rate analysis

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, Savar\'e and Veneroni.