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arXiv · 1507.02104

Generalisation of the Eyring-Kramers transition rate formula to irreversible diffusion processes

Freddy Bouchet·Julien Reygner
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Abstract

In the small noise regime, the average transition time between metastable states of a reversible diffusion process is described at the logarithmic scale by Arrhenius' law. The Eyring-Kramers formula classically provides a subexponential prefactor to this large deviation estimate. For irreversible diffusion processes, the equivalent of Arrhenius' law is given by the Freidlin-Wentzell theory. In this paper, we compute the associated prefactor and thereby generalise the Eyring-Kramers formula to irreversible diffusion processes. In our formula, the role of the potential is played by Freidlin-Wentzell's quasipotential, and a correction depending on the non-Gibbsianness of the system along the instanton is highlighted. Our analysis relies on a WKB analysis of the quasistationary distribution of the process in metastable regions, and on a probabilistic study of the process in the neighbourhood of saddle-points of the quasipotential.

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Freddy Bouchet, Julien Reygner. 2015-07-08. Generalisation of the Eyring-Kramers transition rate formula to irreversible diffusion processes. https://doi.org/10.1007/s00023-016-0507-4

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