# Cyclization of a Polymer: A First Passage Problem for a Non-Markovian Process

Source: [Cyclization of a Polymer: A First Passage Problem for a Non-Markovian Process](<https://www.sota2.com/research/paper/68fa25b12c2a3760193b2de9>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T10:54:26.960Z

Authors: I.M. Sokolov

Published: 2002-07-05T14:41:00.000Z

## Abstract

We discuss a problem of cyclization of a polymer molecule, which is an important example of reaction in a system showing strongly non-Markovian behavior on the timescales of interest. We show that the knowledge of the joint three-time probability distribution of the end-to-end distance is sufficient for the full description of the cyclization kinetics, so that the survival probability follows rigorously as a solution of the Volterra integral equation. The corresponding kinetics can easily be evaluated numerically. We moreover discuss how do some well-known approximations appear from this exact scheme due to decoupling.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/cond-mat/0207159>)

[PDF](<https://arxiv.org/pdf/cond-mat/0207159.pdf>)