Arrhenius law for interacting diffusive systems

Abstract

Finding the mean time it takes for a particle to escape from a meta-stable state due to thermal fluctuations is a fundamental problem in physics, chemistry and biology. For weak thermal noise, the mean escape time is captured by the Arrhenius law (AL). Despite its ubiquity in nature and wide applicability in practical engineering, the problem is typically limited to single particle physics. Finding a generalized form of the AL for interacting particles has eluded solution for a century. Here, we tackle this outstanding problem and generalize the AL to a class of interacting diffusive systems within the framework of the macroscopic fluctuation theory. The generalized AL is shown to conform a non-trivial yet elegant form that depends crucially on the particle density and inter-particle interactions. We demonstrate our results for the paradigmatic exclusion and inclusion processes to underpin the key effects of repulsive and attractive interactions. Intriguingly, we show how to manipulate the mean escape time using not only temperature, but also the particle density.

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• Transition path time over a barrier of a colloidal particle in a viscoelastic bath
• $1/f$ noise in semiconductors arising from the heterogeneous detrapping process of individual charge carriers
• Systematic analysis of critical exponents in continuous dynamical phase transitions of weak noise theories
• Inferring intermediate states by leveraging the many-body Arrhenius law
• Speeding up Brownian escape via intermediate finite potential barriers