Volume 120, Number 3, November 2017
|Number of page(s)||6|
|Section||Interdisciplinary Physics and Related Areas of Science and Technology|
|Published online||01 February 2018|
Anomalous behaviour of mutual information in finite flocks
1 Sackler Centre for Consciousness Science, Department of Informatics, University of Sussex - Brighton, UK
2 School of Computing & Mathematics, Charles Sturt University - Bathurst, NSW, Australia
3 Centre for Research in Complex Systems, Charles Sturt University - Bathurst, NSW, Australia
Received: 14 September 2017
Accepted: 12 January 2018
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 which do not truly break ergodicity 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.
PACS: 89.70.Cf – Entropy and other measures of information / 89.75.-k – Complex systems / 64.60.De – Statistical mechanics of model systems (Ising model, Potts model, field-theory models, Monte Carlo techniques, etc.)
© EPLA, 2018
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