Rich out-of-equilibrium collective dynamics of strongly interacting large assemblies emerge in many areas of science. Some intriguing and not fully understood examples are the glassy arrest in atomic, molecular, or colloidal systems; flocking in natural or artificial active matter; and the organization and subsistence of ecosystems. The learning process, and ensuing amazing performance, of deep neural networks bears resemblance with some of the before-mentioned examples. Quantum mechanical extensions are also of interest. In exact or approximate manner, the evolution of these systems can be expressed in terms of a dynamical mean-field theory that not only captures many of their peculiar effects but also has predictive power. This short review presents a summary of recent developments of this approach with emphasis on applications on the examples mentioned above.

中文翻译：

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动态平均场方法的最新应用


许多科学领域都出现了强相互作用的大型组件的丰富的不平衡集体动力学。一些有趣但尚未完全理解的例子是原子、分子或胶体系统中的玻璃态逮捕；天然或人工活性物质植绒；以及生态系统的组织和生存。深度神经网络的学习过程以及随之而来的惊人性能与前面提到的一些例子有相似之处。量子力学的扩展也很有趣。以精确或近似的方式，这些系统的演化可以用动态平均场理论来表达，该理论不仅捕获了它们的许多特殊效应，而且还具有预测能力。这篇简短的评论总结了这种方法的最新发展，重点是上述示例的应用。