  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.
