输运过程的非平衡麦克斯韦妖NEMD模拟：I. 将剪切黏度外推至流体力学极限
Nonequilibrium Maxwell-Demon NEMD formalism for transport: I. Extrapolating shear viscosity to the hydrodynamic limit
- University of Missouri（密苏里大学）
- Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究提出麦克斯韦妖非平衡分子动力学方法测量伦纳德-琼斯流体的剪切黏度，证实其结果一致，且三维系统剪切黏度随粒子数增加以1/√N趋近流体力学极限。
AI中文摘要：
我们提出一种麦克斯韦妖非平衡分子动力学（NEMD）方法，用于测量伦纳德-琼斯（Lennard-Jones）流体的剪切黏度。模拟单元在x方向被划分为两个宽度为w的区域，粒子可在两侧自由移动。该麦克斯韦妖通过施加总加速度g_total维持两个区域在y方向的平均粒子速度大小相等、方向相反（±u_p），其中g_total包含总力平衡项以及粒子跨边界扩散的修正项。维持非平衡稳态（NESS）所需的动量弛豫率为γ=g_total/u_p。研究表明，驱动的速度分布并非由约束在x方向逐点施加，而是由流体的区域流体力学响应决定。对于该剪切几何，欧拉平板中测得的NESS分布可由分段抛物线形式很好地表示，这与平面泊肃叶流类似。该抛物线分布可通过对剪切流体做功估算运动黏度，公式为ν_para=γ_total w²/12；还可通过诺伊-胡佛（Nosé–Hoover）恒温器移除的热量估算熵产，该恒温器用于维持每个区域的平均温度恒定。在一次代表性运行中，做功与熵产的估算结果偏差在0.6%以内，证实了麦克斯韦妖提供的机械功与恒温器移除的热量之间的一致性。一旦移除NESS驱动，抛物线速度分布会以指数形式快速弛豫为正弦形式，即自然横向动量扩散本征模。这些结果确立了麦克斯韦妖剪切方法是一种直接的NEMD途径，可通过动量扩散、功和熵平衡获取剪切黏度。我们针对三维系统中不断增加的粒子数N的研究结果表明，剪切黏度会以1/√N的形式趋近于渐近值（流体力学极限）。
英文摘要：
The Maxwell-Demon nonequilibrium molecular dynamics method for measuring the shear viscosity divides the fluid simulation cell into two regions of width w in the $x$-direction, with the particles allowed to move freely between the two sides. The Demon maintains equal and opposite regional average particle velocities in the $y$-direction by applying an acceleration needed to sustain the nonequilibrium steady state (NESS), which includes both total force balance and an instantaneous correction for diffusion of particles across boundaries. We show that the driven velocity profile in x is a natural hydrodynamic response and not imposed by the constraint. For the present shear geometry, the measured NESS profile in Eulerian slabs is represented accurately by a piecewise parabolic form, reminiscent of planar Poiseuille flow. The parabolic profile gives an estimate of the kinematic viscosity from work done on the shearing fluid, as well as an entropy production estimate, derived from heat removal by the Nosé-Hoover thermostat that keeps each regional average temperature constant. We show that the mechanical work supplied by the Demon equals the heat removed by the thermostat. Once NESS driving is removed, the parabolic velocity profile relaxes exponentially in short order to sinusoidal, the natural transverse momentum-diffusion eigenmode. Our Maxwell-Demon shear method provides a direct NEMD formalism for obtaining shear viscosity from momentum diffusion, work, and entropy balances. Our results in three dimensions for increasing system size $N$ (the number of particles) demonstrate that shear viscosity approaches an asymptote (the so-called hydrodynamic limit) as $N^{-1/3}$.
