Title: How to derive a predictive active field theory: a step-by-step tutorial Show Chinese title

Title: 如何推导预测性主动场理论：分步教程

Abstract: The study of active soft matter has developed into one of the most rapidly growing areas of physics. Field theories, which can be developed either via phenomenological considerations or by coarse-graining of a microscopic model, are a very useful tool for understanding active systems. Here, we provide a detailed review of a particular coarse-graining procedure, the interaction-expansion method (IEM). The IEM allows for the systematic microscopic derivation of predictive field theories for systems of interacting active particles. We explain in detail how it can be used for a microscopic derivation of active model B+, which is a widely used scalar active matter model. Extensions and possible future applications are also discussed. Show Chinese abstract

Abstract: 主动软物质的研究已经发展成为物理学中最迅速增长的领域之一。 通过现象学考虑或对微观模型进行粗粒化，可以建立场论，这是理解主动系统的一种非常有用的工具。 在这里，我们详细回顾了一种特定的粗粒化过程，即相互作用展开方法（IEM）。 IEM 允许系统地从微观层面推导出相互作用活性粒子系统的预测性场论。 我们详细解释了如何将其用于主动模型 B+ 的微观推导，该模型是一个广泛使用的标量主动物质模型。 还讨论了其扩展和可能的未来应用。