发表机构
University of Aberdeen（阿伯丁大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文综述复杂系统中的高阶相互作用，区分机制、行为与表示，提出可约性框架，并讨论检测与推断方法及开放问题。
AI 中文摘要
高阶相互作用以无法分解为成对贡献的方式耦合三个或更多元素。在多样的复杂系统中，它们产生引人注目的集体行为，如爆炸性同步、不连续转变和稳定性改变。这种行为以及用多体术语描述的表述都不能确立多体机制，因为两者都依赖于系统的表示方式。本综述区分了三个问题：什么机制支配系统，它产生什么行为，以及任一者如何被表示？表示涵盖包含哪些变量以及它们之间的关系如何被编码。我们考察直接的多体机制、模仿它们的非线性但成对的机制，以及通过共享环境或消除变量的间接路径，连同时间聚合——一种观察的伪影而非机制。相同的行为可能源于不同的机制，而给定的高阶机制没有普遍的行为后果。然后我们阐述可约性，即高阶模型能否被低阶模型替代的问题，将其视为源模型与可接受的低阶模型类别之间的比较，相对于目标和容差。目标可以是微观规则、可观测量或定性特征。信息论和推断方法被综述为检测高阶依赖性、检验低阶替代方案和重建相互作用结构的互补工具。然而，仅凭观测数据通常无法确立机制。最后，我们指出在将机制与可测量特征联系起来、粗粒化、可辨识性和因果性，以及将约化扩展到平均场之外方面的开放问题。(删节)
英文摘要
Higher-order interactions couple three or more elements in ways that cannot be decomposed into pairwise contributions. In diverse complex systems they produce striking collective behaviours such as explosive synchronization, discontinuous transitions and altered stability. Neither such behaviour nor a description written in many-body terms establishes a many-body mechanism, since both depend on how the system is represented. This review distinguishes three questions: what mechanism governs the system, what behaviour does it produce, and how is either represented? Representation covers both which variables are included and how relations among them are encoded. We examine direct many-body mechanisms, nonlinear but pairwise mechanisms that mimic them, and indirect routes through shared environments or eliminated variables, together with temporal aggregation, an artefact of observation rather than a mechanism. The same behaviour can arise from different mechanisms, and a given higher-order mechanism has no universal behavioural consequence. We then formulate reducibility, the question of whether a higher-order model can be replaced by a lower-order one, as a comparison between a source model and an admissible class of lower-order models, relative to a target and a tolerance. The target may be a microscopic rule, an observable or a qualitative feature. Information-theoretic and inferential methods are reviewed as complementary tools for detecting higher-order dependence, testing lower-order alternatives and reconstructing interaction structure. However, observational data alone generally cannot establish the mechanism. We close by identifying open problems in linking mechanisms to measurable signatures, coarse-graining, identifiability and causality, and in extending reductions beyond mean field. (Abridged)
Comments30 pages, 1 figure, 1 table, review paper
