Local equilibrium in bird flocks

TL;DR

This study introduces a maximum entropy-based dynamical inference method to analyze starling flocks, revealing that local bird alignment occurs faster than network rearrangements, indicating a state of local quasi-equilibrium.

Contribution

The paper presents a novel inference technique accommodating network dynamics, demonstrating local quasi-equilibrium in bird flocks and validating equilibrium assumptions.

Findings

Local alignment occurs faster than neighbor rearrangement.

Equilibrium inference aligns with dynamical inference results.

Bird orientations are in local quasi-equilibrium.

Abstract

The correlated motion of flocks is an instance of global order emerging from local interactions. An essential difference with analogous ferromagnetic systems is that flocks are active: animals move relative to each other, dynamically rearranging their interaction network. The effect of this off-equilibrium element is well studied theoretically, but its impact on actual biological groups deserves more experimental attention. Here, we introduce a novel dynamical inference technique, based on the principle of maximum entropy, which accodomates network rearrangements and overcomes the problem of slow experimental sampling rates. We use this method to infer the strength and range of alignment forces from data of starling flocks. We find that local bird alignment happens on a much faster timescale than neighbour rearrangement. Accordingly, equilibrium inference, which assumes a fixed interaction network, gives results consistent with dynamical inference. We conclude that bird orientations are in a state of local quasi-equilibrium over the interaction length scale, providing firm ground for the applicability of statistical physics in certain active systems.