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<p>We develop a minimal theoretical model that reveals a structured steady-state flux field with four alternating local circulation, a phenomenon we refer to as <i>quadrupolar gyration</i>. A passive Brownian particle is confined to move in a ring-shaped trap and driven far from equilibrium solely by anisotropic thermal fluctuations from two orthogonal heat baths held at different temperatures. By breaking detailed balance, this fundamental temperature anisotropy induces a robust nonequilibrium steady state characterized by probability currents of the particle’s motion. Remarkably, these currents self-organize into a distinctive quadrupolar vortex pattern, providing a clear signature of emergent symmetry breaking, irreversible entropy production, and coherent motion in minimal passive systems. Our theoretical predictions, based on the narrow-ring approximation and the assumption of small thermal anisotropy, are validated by numerical simulations.</p>

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Quadrupolar gyration of a Brownian particle in a confining ring

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月3日

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  • Iman Abdoli,
  • Hartmut Löwen

摘要

We develop a minimal theoretical model that reveals a structured steady-state flux field with four alternating local circulation, a phenomenon we refer to as quadrupolar gyration. A passive Brownian particle is confined to move in a ring-shaped trap and driven far from equilibrium solely by anisotropic thermal fluctuations from two orthogonal heat baths held at different temperatures. By breaking detailed balance, this fundamental temperature anisotropy induces a robust nonequilibrium steady state characterized by probability currents of the particle’s motion. Remarkably, these currents self-organize into a distinctive quadrupolar vortex pattern, providing a clear signature of emergent symmetry breaking, irreversible entropy production, and coherent motion in minimal passive systems. Our theoretical predictions, based on the narrow-ring approximation and the assumption of small thermal anisotropy, are validated by numerical simulations.