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.

References in corpus (8)

• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• The Exclusion Process: A paradigm for non-equilibrium behaviour
• Mapping out of equilibrium into equilibrium in one-dimensional transport models
• Activated escape of a self-propelled particle from a metastable state
• Dynamical symmetry breaking and phase transitions in driven diffusive systems
• Survival of a static target in a gas of diffusing particles with exclusion
• Numerical Study of Continuous and Discontinuous Dynamical Phase Transitions for Boundary Driven Systems
• Geometrical Interpretation of Dynamical Phase Transitions in Boundary Driven Systems

Cited by in corpus (8)

• Large deviations in statistics of the local time and occupation time for a run and tumble particle
• Emerging universality classes in thermally-assisted activation of interacting diffusive systems: A perturbative hydrodynamic approach
• Experimental measurement of mean transition path velocities of colloidal particles surmounting energy barriers
• 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