# Polymer translocation across a corrugated channel: Fick-Jacobs approximation extended beyond the mean first passage time

## TL;DR

This paper extends the Fick-Jacobs approximation to analyze the translocation dynamics of a Gaussian polymer in a corrugated channel, focusing on the variability of first passage times beyond mean values.

## Contribution

It introduces a generalized Fick-Jacobs approach to evaluate the coefficient of variation of first passage times, revealing the broadness of the distribution in polymer translocation.

## Key findings

- Coefficient of variation never drops below 1
- First passage time distribution can be very broad
- Mean first passage time alone is insufficient for characterization

## Abstract

Polymer translocation across a corrugated channel is a paradigmatic stochastic process encountered in diverse systems. The instance of time when a polymer first arrives to some prescribed location defines an important characteristic time scale for various phenomena, which are triggered or controlled by such an event. Here we discuss the translocation dynamics of a Gaussian polymer in a periodically-corrugated channel using an appropriately generalized Fick-Jacobs approach. Our main aim is to probe an effective broadness of the first passage time distribution (FPTD), by determining the so-called coefficient of variation $\gamma$ of the FPTD, defined as the ratio of the standard deviation versus the mean first passage time (MFPT). We present a systematic analysis of $\gamma$ as a function of a variety of system's parameters. We show that $\gamma$ never significantly drops below 1 and, in fact, can attain very large values, implying that the MFPT alone cannot characterize the first-passage statistics of the translocation process exhaustively well.