Kramers' law: Validity, derivations and generalisations

By Nils Berglund. 2011

191 citations recorded by the source corpus.

Kramers' law describes the mean transition time of an overdamped Brownian par- ticle between local minima in a potential landscape. We review dierent approaches that have been followed to obtain a mathematically rigorous proof of this formula. We also discuss some generalisations, and a case in which Kramers' law is not valid. This review is written for both mathematicians and theoretical physicists, and endeavours to link concepts and terminology from both elds.

Subfields: Statistical and Nonlinear Physics

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In Statistical and Nonlinear Physics

1. Alessandro Achille
2. Giovanni Paolini
3. Stefano Soatto
4. Julien Reygner
5. Freddy Bouchet

Citations in the corpus

• Where is the Information in a Deep Neural Network? (2019, methodology): “We can formalize this reasoning using a slight reformulation of the Eyring–Kramers law [4] for stochastic processes in the form of eq.”
• Generalisation of the Eyring–Kramers Transition Rate Formula to Irreversible Diffusion Processes (2015, methodology): “We refer to the survey by Berglund [6] for a review of mathematical approaches to the Eyring-Kramers formula, and highlight that the study of such formulas for general equilibrium systems remains an active field in mathematics, see for instance [7, 13, 9] for degenerate potentials, [40] for the rela”