结构粘性、热波与 Mpemba 效应从扩展结构动力学
Structural Viscosity, Thermal Waves, and the Mpemba Effect from Extended Structural Dynamics
AI总结：
本文提出扩展结构动力学理论，通过双曲抛物线输运方程解释结构粘性、热波及Mpemba效应，揭示各向异性输运和非傅里叶热现象的微观机制。
摘要：
经典流体力学基于点粒子理想化，导致抛物线输运方程、无限信号速度以及无法捕捉有限时间弛豫、各向异性输运或非傅里叶热现象。本文引入扩展结构动力学（ESD），是一种动力学框架，其中构成要素被描述为具有方向、角动量和内部变形模式的空间扩展物体。从扩展玻尔兹曼方程出发，通过BGK闭合的 Chapman-Enskog展开，得到两个双曲抛物线输运定律：一个动态自旋方程将方向弛豫与流体涡旋耦合，另一个热流弛豫方程具有结构热导率。这些方程预测动量和热的有限传播速度、内在冲击波正则化、各向异性输运和热波。自旋方程提供了微极流体理论的动能推导，而热流方程为Cattaneo Vernotte行为提供了微观基础。定量估计表明结构贡献可以主导经典输运系数。BGK闭合保持了扩展相空间的定性几何结构，并捕捉到正确的尺度；方向弛豫时间与李雅普诺夫不稳定性之间的联系被独立建立。所得到的尺度定律源自旋转-平动耦合。预测包括球状椭球体的Mpemba临界时间以及不对称分子的冲击波宽度，两者均可通过现有技术进行检验。
英文摘要：
Classical hydrodynamics rests on the point-particle idealization, leading to parabolic transport equations, infinite signal speeds, and the inability to capture finite time relaxation, anisotropic transport, or non Fourier thermal phenomena. This work introduces Extended Structural Dynamics (ESD), a kinetic framework in which constituents are described as spatially extended objects possessing orientation, angular momentum, and internal deformation modes. Starting from an extended Boltzmann equation, a Chapman Enskog expansion with BGK closure yields two hyperbolic parabolic transport laws: a dynamical spin equation coupling orientational relaxation to fluid vorticity, and a heat flux relaxation equation with structural thermal conductivity. These equations predict finite propagation speeds for momentum and heat, intrinsic shock regularization, anisotropic transport, and thermal waves. The spin equation provides a kinetic derivation of micropolar fluid theory, while the heat flux equation supplies a microscopic foundation for Cattaneo Vernotte behavior. Quantitative estimates indicate structural contributions can dominate classical transport coefficients. The BGK closure preserves the qualitative geometric structure of extended phase space and captures correct scaling; the connection between the orientational relaxation time and Lyapunov instability is established independently. The resulting scaling laws follow from rotational-translational coupling. Predictions include Mpemba crossover time for colloidal ellipsoids and shock width for asymmetric molecules, both testable with existing techniques.
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