The propagation of gradient flow structures from microscopic to macroscopic models is a topic of high current interest. In this paper, we discuss this propagation in a model for the diffusion of particles interacting via hard-core exclusion or short-range repulsive potentials. We formulate the microscopic model as a high-dimensional gradient flow in the Wasserstein metric for an appropriate free-energy functional. Then we use the JKO approach to identify the asymptotics of the metric and the free-energy functional beyond the lowest order for single particle densities in the limit of small particle volumes by matched asymptotic expansions. While we use a propagation of chaos assumption at far distances, we consider correlations at small distance in the expansion. In this way, we obtain a clear picture of the emergence of a macroscopic gradient structure incorporating corrections in the free-energy functional due to the volume exclusion.

中文翻译：

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排除体积效应的 Fokker-Planck 方程的粗粒度保留梯度流结构

梯度流动结构从微观模型到宏观模型的传播是当前备受关注的话题。在本文中，我们在通过硬核排斥或短程排斥势相互作用的粒子扩散模型中讨论了这种传播。我们将微观模型制定为 Wasserstein 度量中的高维梯度流，以获得适当的自由能泛函。然后，我们使用 JKO 方法通过匹配的渐近展开来识别度量的渐近性和超出单个粒子密度最低阶的自由能泛函。虽然我们在远距离使用混沌传播假设，但我们在扩展中考虑了小距离的相关性。这样，