Anomalous Behaviour of Mutual Information in Finite Flocks

TL;DR

This paper reveals that in finite flocks, mutual information can diverge as noise decreases, challenging the idea that it peaks at criticality in large systems, with implications for finite-size out-of-equilibrium systems.

Contribution

It demonstrates that mutual information behavior in finite flocks differs from large systems, showing divergence as noise approaches zero, contrary to prior assumptions.

Findings

Mutual information may diverge as noise tends to zero in finite flocks.

Mutual information does not necessarily peak at criticality in finite systems.

Implications for using mutual information to locate phase transitions in finite, out-of-equilibrium systems.

Abstract

The existing consensus is that flocks are poised at criticality, entailing long correlation lengths and a maximal value of Shannon mutual information in the large-system limit. We show, by contrast, that for finite flocks in the long observation time limit, mutual information may not only fail to peak at criticality---as observed for other critical systems---but also diverge as noise tends to zero. This result carries implications for other finite-size, out-of-equilibrium systems, where observation times may vary widely compared to time scales of internal system dynamics; thus it may not be assumed that mutual information locates the phase transition.