费舍尔信息动力学：用于相空间排序的运动学框架及其在激波层和湍流中的应用
Fisher Information Dynamics: A Kinematic Framework for Phase Space Ordering with Applications to Shock Layers and Turbulence
浏览论文内容
中文总结 AI 辅助
该研究建立了基于费舍尔信息产生率的相空间排序运动学框架，推导相关分解与定理，经激波层和湍流模拟验证，为非平衡系统序动力学分析提供诊断预测工具。
中文摘要 AI 辅助
我们建立了一种基于费舍尔信息产生率的相空间排序运动学框架。从连续性方程出发，我们将其分解为四项：各向同性收缩、无迹剪切、散度梯度和边界通量。将其推广到Fokker-Planck方程，我们证明了扩散耗散项的严格非正性。我们证明了一个涡旋独立性定理：纯旋转速度场不会改变序度规。我们推导了每个变形项的显式几何符号判据，可用于预测序的产生或破坏。通过Burgers激波层的精确解，我们揭示了压缩项与散度梯度项之间的逐点恒等式，该恒等式构成了三项平衡的基础。二维湍流模拟验证了剪切耗散平衡。我们进一步表明，相关Wasserstein梯度流的变分稳态隐含了分解平衡。该框架为分析非平衡系统中的序动力学提供了一种诊断和预测工具。
英文摘要
Order here denotes the sharpness of probability-density gradients as quantified by Fisher information, distinct from thermodynamic order parameters. A kinematic framework for phase space ordering is established based on the Fisher information production rate, which possesses a rigorous thermodynamic foundation through the de Bruijn identity, Stam inequality, and dissipation theorem. A four-term decomposition into isotropic contraction, traceless shear, divergence gradient, and boundary flux is derived from the continuity equation. Extending to the Fokker-Planck equation, the non-positivity of the diffusive dissipation term is proved, with strict negativity for non-uniform densities. A vorticity-independence theorem shows that purely rotational velocity fields do not alter the order measure, and explicit geometric sign criteria enable prediction of where order is generated or destroyed. Through exact solutions of the Burgers shock layer, a pointwise identity between compression and divergence-gradient contributions is uncovered, underlying the three-term balance. In two-dimensional incompressible turbulence, a statistical two-term equilibrium (vanishing time-averaged production) is established as the null hypothesis: the conservative reference state from which three-dimensional turbulence departs through vortex stretching. Variational steady states of the associated Wasserstein gradient flow imply vanishing of the total production rate. This framework provides a diagnostic and predictive tool for analyzing ordering dynamics in non-equilibrium systems.
发表机构
- Institute of Aerospace Technology, China Aerodynamics Research and Development Center（中国空气动力研究与发展中心航空航天技术研究所）
机构由 AI 辅助整理，请以论文原文为准。
