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

Abstract

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 power the alignment of spins. 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- 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 tradeoff relationship provides a new perspective for understanding the dynamics of natural flocks and designing optimal artificial flocking systems.

arXiv comment5 (main text)+ 3 (appendix) + 15 (supplemental material) pages, 3+1+7 figures

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• Macroscopic Stochastic Thermodynamics
• Metastability of Discrete-Symmetry Flocks
• Thermodynamically consistent flocking: From discontinuous to continuous transitions
• Time-reversal symmetry breaking in the chemosensory array reveals mechanisms for dissipation-enhanced cooperative sensing
• Quantifying dissipation in flocking dynamics: When tracking internal states matters
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• Irreversibility in Non-reciprocal Chaotic Systems
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• Ultrasensitivity without conformational spread: A mechanical origin for non-equilibrium cooperativity in the bacterial flagellar motor