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

TL;DR

This paper investigates the energy dissipation in flocking behavior within the active Ising model, revealing a cusp in alignment dissipation at the flocking transition, and provides analytical insights into this singular behavior.

Contribution

It introduces an analytical solution for the AIM model showing a maximum in alignment dissipation at the flocking transition, highlighting a fundamental energy-performance tradeoff.

Findings

Alignment dissipation peaks at flocking transition

Exact dependence of dissipation on order parameter derived

Tradeoff between energy cost and flocking performance identified

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.