Most probable transition path in an overdamped system for a finite transition time

TL;DR

This paper rigorously proves that the most probable transition path in a one-dimensional overdamped system has fewer than two turning points, regardless of potential, transition time, or boundary points.

Contribution

It provides a rigorous proof that the most probable transition path in such systems has fewer than two turning points, applicable to all potentials and transition conditions.

Findings

Most probable paths have less than two turning points.

The proof applies universally to any potential and transition time.

The result enhances understanding of transition dynamics in overdamped systems.

Abstract

The most probable transition path in a one-dimensional overdamped system is rigorously proved to possess less than two turning points. The proof is valid for any potentials, transition times, initial and final transition points.