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.

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

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• Dissipation at limited resolutions: Power law and detection of hidden dissipative scales
• Entropy production rate in thermodynamically consistent flocks
• Irreversibility in Non-reciprocal Chaotic Systems
• Heat production in a stochastic system with nonlinear time-delayed feedback
• Entropy production in non-reciprocal polar active mixtures
• Stochastic Thermodynamics of Non-reciprocally Interacting Particles and Fields
• Ultrasensitivity without conformational spread: A mechanical origin for non-equilibrium cooperativity in the bacterial flagellar motor