The First Exit Time Statistics and the Entropic Forces in Single File Diffusion

TL;DR

This paper analytically derives the first exit time statistics for single file diffusion and explores how these relate to the system's entropic forces and displacement, revealing insights into the speed-accuracy trade-off.

Contribution

It provides the first analytical computation of exit time statistics in single file diffusion and links these to entropic forces and system dynamics.

Findings

Analytical formulas for first exit time statistics

Relationship between exit times and entropic forces

Insights into speed-accuracy trade-offs in diffusion

Abstract

Single file systems are simplified models to study effectively one-dimensional physical systems. Here we compute analytically the complete first exit time statistics for an ideal overdamped single file with absorbing boundary conditions. Then we use these results to study the speed-accuracy trade-off characterizing this observable in terms of the means square displacement and the entropic repulsive forces of the system.