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Statistical mechanics for natural flocks of birds

Flocking is a typical example of emergent collective behavior,
where interactions between individuals produce collective
patterns on the large scale. Here we show how a quantitative
microscopic theory for directional ordering in a flock can be
derived directly from field data. We construct the minimally
structured (maximum entropy) model consistent with
experimental correlations in large flocks of starlings. The
maximum entropy model shows that local, pairwise interactions
between birds are sufficient to correctly predict the propagation
of order throughout entire flocks of starlings, with no free
parameters. We also find that the number of interacting neighbors
is independent of flock density, confirming that interactions are
ruled by topological rather than metric distance. Finally, by comparing
flocks of different sizes, the model correctly accounts for the observed
scale invariance of long-range correlations among the fluctuations in flight direction.