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Spherical Boundary Conditions: A Topological Framework for Isotropic Collective Dynamics
Manuel Dedola1, Ludovico Cademartiri1
1Department of Chemistry, Life Sciences and Environmental Sustainability, University of Parma, Parco Area delle Scienze 17 A, Parma 43121, Italy.
The Journal of Physical Chemistry. B
|May 28, 2026
Summary
Standard periodic boundary conditions create artifacts in simulations. Spherical Boundary Conditions (SBC) eliminate these artifacts, restoring accurate simulations of isotropic liquids and their dynamics.
Area of Science:
- Computational physics
- Materials science
- Statistical mechanics
Background:
- Standard periodic boundary conditions (PBC) impose a toroidal topology, leading to spurious long-range temporal correlations.
- These artifacts manifest as lattice-aligned anisotropy in dynamic observables, violating the static-dynamic correspondence (de Gennes narrowing).
Purpose of the Study:
- Introduce Spherical Boundary Conditions (SBC) as a novel topological framework.
- Resolve artifacts caused by PBC and restore accurate simulation of isotropic liquids.
Main Methods:
- Developed SBC using a radial folding map and chaotic boundary remapping.
- Implemented SBC within Brownian dynamics simulations.
- Analyzed static and dynamic correlations and ergodicity.
Main Results:
- SBC eliminates lattice-aligned anisotropy by construction.
- Restores isotropic static and dynamic correlations.
- Recovers the ergodicity and static-dynamic correspondence of the infinite bulk limit on finite domains.
Conclusions:
- SBC effectively acts as a measure-preserving information filter.
- Preserves thermodynamic laws while suppressing artifacts from periodic boundary conditions.
- SBC provides a robust method for accurate simulations of liquids and materials.
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