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  • Letter
  • Open Access

Exact generalized Langevin dynamics of pair coordinates in elastic networks

Shunsuke Ando1, Tomoya Urashita1, Soya Shinkai2, and Tomoshige Miyaguchi1,*

  • *Contact author: mygch@wakayama-u.ac.jp
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Phys. Rev. E 114, L042108 – Published 22 October, 2026

DOI: https://doi.org/10.1103/v5zx-93k9

Abstract

Generalized Langevin equations (GLEs) provide a powerful framework for describing slow dynamics in soft-matter systems, but deriving an exact GLE for a reaction coordinate from an underlying many-body system remains generally difficult. Here, we analytically derive an exact coupled GLE for the overdamped dynamics of two tagged beads in arbitrary harmonic elastic networks. We further derive an exact GLE for their relative coordinate. The memory kernel and effective restoring force are expressed explicitly in terms of the network matrices, thereby providing a systematic reduction of the high-dimensional network dynamics to a pair coordinate. Within the small-displacement approximation, we further derive a GLE for the interbead distance, a central observable in distance-sensitive single-molecule experiments. These results therefore have broad potential applications in modeling proteins and other soft-matter systems.

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Phys. Rev. E 114, L042108– Published 22 October, 2026
  • Received 14 April 2026
  • Accepted 29 September 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal "citation, and DOI.

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