Mason James, Jack Robert L, Bruna Maria
DAMTP, Centre for Mathematical Sciences, University of Cambridge, Cambridge, UK.
Yusuf Hamied Department of Chemistry, University of Cambridge, Cambridge, UK.
Nat Commun. 2025 Jul 1;16(1):6017. doi: 10.1038/s41467-025-60518-6.
The formation of dynamical patterns is one of the most striking features of nonequilibrium physical systems. Recent work has shown that such patterns arise generically from forces that violate Newton's third law, known as nonreciprocal interactions. These nonequilibrium phenomena are challenging for modern theories. Here, we introduce a model mixture of active (self-propelled) and passive (diffusive) particles amenable to exact mathematical analysis. We exploit state-of-the-art methods to derive exact hydrodynamic equations for the particle densities, which reveal effective nonreciprocal couplings between the active and passive species. We study the resulting collective behavior, including the linear stability of homogeneous states and phase coexistence in large systems. This reveals a novel phase diagram with the spinodal associated with active phase separation protruding through the associated binodal, heralding the emergence of dynamical steady states. We analyze these states in the thermodynamic limit of large system size, showing, for example, that sharp interfaces may travel at finite velocities, but traveling phase-separated states are forbidden. The model's mathematical tractability enables precise new conclusions beyond those available by numerical simulation of particle models or field theories.
动力学模式的形成是非平衡物理系统最显著的特征之一。最近的研究表明，这类模式通常源于违反牛顿第三定律的力，即非互易相互作用。这些非平衡现象对现代理论提出了挑战。在此，我们引入一种由主动（自推进）粒子和被动（扩散）粒子组成的模型混合物，它适合进行精确的数学分析。我们利用最先进的方法推导出粒子密度的精确流体动力学方程，这些方程揭示了主动粒子和被动粒子之间有效的非互易耦合。我们研究由此产生的集体行为，包括均匀态的线性稳定性和大系统中的相共存。这揭示了一个新颖的相图，其中与主动相分离相关的旋节线穿过相关的双节线，预示着动态稳态的出现。我们在大系统尺寸的热力学极限下分析这些状态，例如表明尖锐界面可能以有限速度移动，但禁止移动的相分离状态。该模型的数学易处理性使得能够得出超越粒子模型或场论数值模拟所能得到的精确新结论。
