How a finite potential barrier decreases the mean first passage time

TL;DR

This paper shows that introducing a potential barrier in a finite interval can reduce the mean first passage time of a random walker, challenging the intuition that barriers always hinder progress.

Contribution

It provides analytical and simulation evidence that a potential barrier can minimize mean first passage time in a finite potential landscape, a novel insight in stochastic processes.

Findings

Potential barriers can decrease mean first passage time.

Thermal fluctuations enable crossing of barriers.

Barrier-induced acceleration outweighs the cost of activation.

Abstract

We consider the mean first passage time of a random walker moving in a potential landscape on a finite interval, starting and end points being at different potentials. From analytical calculations and Monte Carlo simulations we demonstrate that the mean first passage time for a piecewise linear curve between these two points is minimised by introduction of a potential barrier. Due to thermal fluctuations this barrier may be crossed. It turns out that the corresponding expense for this activation is less severe than the gain from an increased slope towards the end point. In particular, the resulting mean first passage time is shorter than for a linear potential drop between the two points.