# Nonlocality of relaxation rates in disordered landscapes

## TL;DR

This paper reveals that relaxation times in disordered landscapes are influenced by rare trajectories sampling the entire potential, leading to nonlocal effects that affect interpretations of relaxation rates in complex systems.

## Contribution

It analytically and numerically demonstrates the nonlocal dependence of relaxation and hopping times on the global potential landscape in disordered systems.

## Key findings

- Relaxation times are dominated by rare trajectories sampling outside the well.
- Hopping times depend on the entire multiwell potential structure.
- Nonlocal effects are crucial for interpreting relaxation rates in complex systems.

## Abstract

We investigate both analytically and by numerical simulation the relaxation of an overdamped Brownian particle in a 1D multiwell potential. We show that the mean relaxation time from an injection point inside the well down to its bottom is dominated by statistically rare trajectories that sample the potential profile outside the well. As a consequence, also the hopping time between two degenerate wells can depend on the detailed multiwell structure of the entire potential. The nonlocal nature of the transitions between two states of a disordered landscape is important for the correct interpretation of the relaxation rates in complex chemical-physical systems, measured either through numerical simulations or experimental techniques.