Statistical mechanics for natural flocks of birds

TL;DR

This paper applies a maximum entropy model, equivalent to the Heisenberg model, to predict how local interactions among birds in a flock lead to large-scale coordinated flight, revealing scale invariance and topological interaction ranges.

Contribution

It introduces a maximum entropy framework for bird flocking that accurately predicts collective behavior without free parameters, linking it to magnetic models.

Findings

Model predicts propagation of order in bird flocks.

Interactions involve a fixed number of neighbors, not fixed distance.

Model accounts for scale invariance in correlations.

Abstract

Interactions among neighboring birds in a flock cause an alignment of their flight directions. We show that the minimally structured (maximum entropy) model consistent with these local correlations correctly predicts the propagation of order throughout entire flocks of starlings, with no free parameters. These models are mathematically equivalent to the Heisenberg model of magnetism, and define an "energy" for each configuration of flight directions in the flock. Comparing flocks of different densities, the range of interactions that contribute to the energy involves a fixed number of (topological) neighbors, rather than a fixed (metric) spatial range. Comparing flocks of different sizes, the model correctly accounts for the observed scale invariance of long ranged correlations among the fluctuations in flight direction.