For classical many-body systems subject to Brownian dynamics we develop a superadiabatic dynamical density functional theory (DDFT) for the description of inhomogeneous fluids out-of-equilibrium. By explicitly incorporating the dynamics of the inhomogeneous two-body correlation functions we obtain superadiabatic forces directly from the microscopic interparticle interactions. We demonstrate the importance of these nonequilibrium forces for an accurate description of the one-body density by numerical implementation of our theory for three-dimensional hard-spheres in a time-dependent planar potential. The relaxation of the one-body density in superadiabatic-DDFT is found to be slower than that predicted by standard adiabatic DDFT and significantly improves the agreement with Brownian dynamics simulation data. We attribute this improved performance to the correct treatment of structural relaxation within the superadiabatic-DDFT. Our approach provides fundamental insight into the underlying structure of dynamical density functional theories and makes possible the study of situations for which standard approaches fail.

中文翻译：

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非均匀流体动力学的第一性原理超绝热理论

对于受布朗动力学影响的经典多体系统，我们开发了一种超绝热动力学密度泛函理论 (DDFT)，用于描述不均匀的非平衡流体。通过明确结合非均匀二体相关函数的动力学，我们直接从微观粒子间相互作用中获得超绝热力。我们通过数值实现我们在时间相关平面势中的三维硬球理论，证明了这些非平衡力对于准确描述单体密度的重要性。发现超绝热 DDFT 中单体密度的松弛比标准绝热 DDFT 预测的要慢，并且显着提高了与布朗动力学模拟数据的一致性。我们将这种改进的性能归因于对超绝热 DDFT 中结构松弛的正确处理。我们的方法提供了对动态密度泛函理论的基本结构的基本见解，并使研究标准方法失败的情况成为可能。