Active systems are composed of constituents with interactions that are generically nonreciprocal in nature. Such nonreciprocity often gives rise to situations where conflicting objectives exist, such as in the case of a predator pursuing its prey, while the prey attempts to evade capture. This situation is somewhat reminiscent of those encountered in geometrically frustrated systems where conflicting objectives also exist, which result in the absence of configurations that simultaneously minimize all interaction energies. In the latter, a rich variety of exotic phenomena are known to arise due to the presence of accidental degeneracy of ground states. Here, we establish a direct analogy between these two classes of systems. The analogy is based on the observation that nonreciprocally interacting systems with antisymmetric coupling and geometrically frustrated systems have in common that they both exhibit marginal orbits, which can be regarded as a dynamical system counterpart of accidentally degenerate ground states. The former is shown by proving a Liouville-type theorem. These “accidental degeneracies” of orbits are shown to often get “lifted” by stochastic noise or weak random disorder due to the emergent “entropic force” to give rise to a noise-induced spontaneous symmetry breaking, in a similar manner to the order-by-disorder phenomena known to occur in geometrically frustrated systems. Furthermore, we report numerical evidence of a nonreciprocity-induced spin-glass-like state that exhibits a short-ranged spatial correlation (with stretched exponential decay) and an algebraic temporal correlation associated with the aging effect. Our work establishes an unexpected connection between the physics of complex magnetic materials and nonreciprocal matter, offering a fresh and valuable perspective for comprehending the latter.

中文翻译：

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不可逆挫败：时间晶体无序有序现象和自旋玻璃态

主动系统由具有一般非互易性质的相互作用的成分组成。这种非互惠性常常会导致目标存在冲突的情况，例如捕食者追捕猎物，而猎物则试图逃避捕获。这种情况有点让人想起几何受挫系统中遇到的情况，其中也存在相互冲突的目标，这导致缺乏同时最小化所有相互作用能量的配置。在后者中，由于基态的意外简并的存在，已知会出现各种各样的奇异现象。在这里，我们在这两类系统之间建立了直接的类比。该类比基于以下观察：具有反对称耦合的非互易相互作用系统和几何受抑系统的共同点是它们都表现出边缘轨道，这可以被视为意外简并基态的动力系统对应物。前者通过证明刘维尔型定理来证明。这些轨道的“意外简并”被证明经常被随机噪声或弱随机无序“提升”，这是由于出现的“熵力”导致噪声引起的自发对称性破缺，其方式与有序-已知在几何受挫系统中发生的无序现象。此外，我们报告了非互易引起的类自旋玻璃态的数值证据，该态表现出短程空间相关性（具有拉伸指数衰减）和与老化效应相关的代数时间相关性。我们的工作在复杂磁性材料和不可逆物质的物理学之间建立了意想不到的联系，为理解后者提供了一个新鲜而有价值的视角。