Density functional theory (DFT) is a powerful theoretical tool widely used in such diverse fields as computational condensed-matter physics, atomic physics and quantum chemistry. DFT establishes that a system of $N$ interacting electrons can be described uniquely by its single-particle density $n(\boldsymbol{r})$ , instead of the $N$ -body wave function, yielding an enormous gain in terms of computational speed and memory storage space. Here, we use time-dependent DFT to show that a classical collisionless plasma can always, in principle, be described by a set of fluid equations for the single-particle density and current. The results of DFT guarantee that an exact closure relation, fully reproducing the Vlasov dynamics, necessarily exists, although it may be complicated (non-local in space and time, for instance) and difficult to obtain in practice. This goes against the common wisdom in plasma physics that the Vlasov and fluid descriptions are mutually incompatible, with the latter inevitably missing some ‘purely kinetic’ effects.

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无碰撞等离子体的密度泛函理论——流体和动力学方法的等效性

密度泛函理论（DFT）是一种强大的理论工具，广泛应用于计算凝聚态物理、原子物理和量子化学等不同领域。DFT 建立了一个系统 $N$ 相互作用的电子可以通过其单粒子密度来唯一描述 $n(\boldsymbol{r})$ , 而不是 $N$ -体波函数，在计算速度和内存存储空间方面产生了巨大的收益。在这里，我们使用时间相关的 DFT 来表明，原则上，经典的无碰撞等离子体总是可以通过一组用于单粒子密度和电流的流体方程来描述。DFT 的结果保证了完全再现 Vlasov 动力学的精确闭合关系必然存在，尽管它可能很复杂（例如在空间和时间上是非局部的）并且在实践中难以获得。这违背了等离子体物理学中的常识，即弗拉索夫和流体描述是相互不相容的，后者不可避免地会丢失一些“纯动力学”效应。