Spherical Boundary Conditions: A Topological Framework for Isotropic Collective Dynamics

Standard periodic boundary conditions (PBC) impose a toroidal topology on simulation domains. While geometrically flat, this topology allows for coherent reentrant self-interactions that preserve spurious long-range temporal correlations. We show that these topological artifacts manifest as strong, lattice-aligned anisotropy in collective dynamic observables, rendering scalar relaxation rates direction-dependent even at near-particle length scales, thereby violating the static-dynamic correspondence of isotropic liquids (de Gennes narrowing). To resolve this, we introduce Spherical Boundary Conditions (SBC), a topological framework that replaces the periodic torus with a mixing quotient space. SBC is defined by a radial folding map coupled to a boundary remapping driven by deterministic chaos. This construction effectively acts as a measure-preserving information filter: it preserves thermodynamic conservation laws, while suppressing the Lagrangian memory responsible for periodic artifacts. Using Brownian dynamics simulations, we demonstrate that SBC eliminates lattice-aligned anisotropy by construction, recovering isotropic static and dynamic correlations and effectively restoring the ergodicity and static-dynamic correspondence of the infinite bulk limit on a finite support.