Physical foundation and consistent formulation of atomic-level fluxes in transport processes
Physical foundation and consistent formulation of atomic-level fluxes in transport processes
复制标题
传输过程中原子级通量的物理基础和一致公式
作者：
Youping Chen;Adrian Diaz
欧文和柯克伍德从经典统计力学的原理中推导出输运方程，使用狄拉克δ来定义局部密度。由此，获得了以分子变量表示的通量公式。欧文和柯克伍德的形式主义启发了许多公式。然而，许多后来的发展认为用连续的体积加权平均函数代替狄拉克δ更严格，随后将通量定义为体积密度。虽然这些体积平均通量公式已经主导了几十年的文献，并广泛应用于流行的分子动力学（MD）软件，他们是一个偏离完善的物理概念的通量。在这项工作中，我们回顾了历史的发展，导致统一的物理概念的通量运输现象。然后，我们使用MD模拟表明，这些流行的通量公式既不守恒动量也不守恒能量，也不产生与其物理定义一致的通量。我们还使用两种不同的方法来获得一般的多体势通量。结果表明，原子通量公式与通量的物理定义和守恒定律完全一致。
Irving and Kirkwood derived the transport equations from the principles of classical statistical mechanics using the Dirac delta to define local densities. Thereby, formulas for fluxes were obtained in terms of molecular variables. The Irving and Kirkwood formalism has inspired numerous formulations. Many of the later developments, however, considered it more rigorous to replace the Dirac delta with a continuous volume-weighted averaging function and subsequently defined fluxes as a volume density. Although these volume-averaged flux formulas have dominated the literature for decades and are widely implemented in popular molecular dynamics (MD) software, they are a departure from the well-established physical concept of fluxes. In this work, we review the historical developments that led to the unified physical concept of fluxes for transport phenomena. We then use MD simulations to show that these popular flux formulas conserve neither momentum nor energy; nor do they produce fluxes that are consistent with their physical definitions. We also use two different approaches to derive fluxes for general many-body potentials. The results of the formulation show that atomistic formulas for fluxes can be fully consistent with the physical definitions of fluxes and conservation laws.