The generic alignment conjecture states that for almost every initial data on the torus solutions to the Cucker–Smale system with a strictly local communication align to the common mean velocity. In this note, we present a partial resolution of this conjecture using a statistical mechanics approach. First, the conjecture holds in full for the sticky particle model representing, formally, infinitely strong local communication. In the classical case, the conjecture is proved when N, the number of agents, is equal to 2. It follows from a more general result, stating that for a system of any size for almost every data at least two agents align. The analysis is extended to the open space \(\mathbb {R}^n\) in the presence of confinement and potential interaction forces. In particular, it is shown that almost every non-oscillatory pair of solutions aligns and aggregates in the potential well.

通用对齐猜想指出，对于具有严格本地通信的 Cucker-Smale 系统的环面解的几乎每个初始数据，都与共同平均速度对齐。在这篇文章中，我们使用统计力学方法提出了这个猜想的部分解决方案。首先，该猜想完全适用于代表形式上无限强的本地通信的粘性粒子模型。在经典情况下，当代理数量N等于 2 时，该猜想得到证明。它是从一个更一般的结果得出的，表明对于任何大小的系统，几乎每个数据都至少有两个代理对齐。该分析扩展到存在约束和潜在相互作用力的开放空间\(\mathbb {R}^n\) 。特别是，它表明几乎所有非振荡解对都在势阱中对齐和聚集。