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The energy cost for flocking of active spins: the cusped dissipation maximum at the flocking transition

Qiwei YuYuhai Tu
May 2022
摘要
We study the energy cost of flocking in the active Ising model (AIM) and showthat besides the energy cost for self-propelled motion, an additional energydissipation is required to power the alignment of spins. We find that thisadditional alignment dissipation reaches its maximum at the flocking transitionpoint in the form of a cusp with a discontinuous first derivative with respectto the control parameter. To understand this singular behavior, we analyticallysolve the two- and three-site AIM models and obtain the exact dependence of thealignment dissipation on the flocking order parameter and control parameter,which explains the cusped dissipation maximum at the flocking transition. Ourresults reveal a trade-off between the energy cost of the system and itsperformance measured by the flocking speed and sensitivity to externalperturbations. This tradeoff relationship provides a new perspective forunderstanding the dynamics of natural flocks and designing optimal artificialflocking systems.
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