Energy Cost for Flocking of Active Spins: The Cusped Dissipation Maximum at the Flocking Transition.
Energy Cost for Flocking of Active Spins: The Cusped Dissipation Maximum at the Flocking Transition.
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DOI：
10.1103/physrevlett.129.278001
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发表时间：
2022-12-30
影响因子：
8.6
通讯作者：
Tu, Yuhai
中科院分区：
文献类型：
--
作者：
Yu, Qiwei;Tu, Yuhai
我们研究了主动伊辛模型(AIM)中群集的能量代价，结果表明，除了自行进运动的能量代价外，为了维持群集秩序，还需要一个额外的能量耗散来排列自旋。我们发现，这种额外的排列耗散在植群转变点处以尖点的形式达到最大值，该尖点相对于控制参数具有不连续的一阶导数。为了理解这一奇异行为，我们解析地求解了两位点和三位点的AIM模型，得到了取向耗散与簇集序参数和控制参数的精确依赖关系，这解释了在簇集转变处的尖点耗散最大值。我们的结果揭示了系统的能量成本和通过群集速度和对外部扰动的敏感度来衡量其性能之间的权衡。这种权衡关系为理解天然集群的动态和设计最优的人工集群系统提供了一个新的视角。
We study the energy cost of flocking in the active Ising model (AIM) and show that besides the energy cost for self-propelled motion, an additional energy dissipation is required to align spins in order to maintain the flocking order. We find that this additional alignment dissipation reaches its maximum at the flocking transition point in the form of a cusp with a discontinuous first derivative with respect to the control parameter. To understand this singular behavior, we analytically solve the two-site and three-site AIM models and obtain the exact dependence of the alignment dissipation on the flocking order parameter and control parameter, which explains the cusped dissipation maximum at the flocking transition. Our results reveal a trade-off between the energy cost of the system and its performance measured by the flocking speed and sensitivity to external perturbations. This trade-off relationship provides a new perspective for understanding the dynamics of natural flocks and designing optimal artificial flocking systems.