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Consistent projection of Langevin dynamics: Preserving thermodynamics and kinetics in coarse-grained models

Vahid Nateghi1, Lara Neureither2, Selma Moqvist3, Carsten Hartmann2, Simon Olsson3, and Feliks Nüske1,*

  • *Contact author: nueske@mpi-magdeburg.mpg.de
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Phys. Rev. E 113, 055308 – Published 28 May, 2026

DOI: https://doi.org/10.1103/wckl-dz9d

Abstract

Coarse graining (CG) is an important task for efficient modeling and simulation of complex multiscale systems, such as the conformational dynamics of biomolecules. This work presents a projection-based coarse-graining formalism for general underdamped Langevin dynamics. Following the Zwanzig projection approach, we derive a closed-form expression for the coarse-grained dynamics. In addition, we show how the generator extended dynamic mode decomposition method, which was developed in the context of Koopman operator methods, can be used to model the CG dynamics and evaluate its kinetic properties, such as transition timescales. Finally, we combine our approach with thermodynamic interpolation, a generative approach to transform samples between thermodynamic conditions, to extend the scope of the approach across thermodynamic states without repeated numerical simulations. Using a two-dimensional model system, we demonstrate that the proposed method allows to accurately capture the thermodynamic and kinetic properties of the full-space model.

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Outline

Information

Phys. Rev. E 113, 055308– Published 28 May, 2026
  • Received 2 December 2025
  • Accepted 6 May 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. Open access publication funded by Max Planck Society.

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