title: Local equilibrium in bird flocks.
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.
authors.affiliation: Laboratoire de physique statistique, CNRS, UPMC and École normale supérieure, 24, rue Lhomond, Paris, France.
authors.forename: Thierry
authors.initials: T
authors.lastname: Mora
authors.affiliation: Laboratoire de physique théorique, CNRS, UPMC and École normale supérieure, 24, rue Lhomond, Paris, France.
authors.forename: Aleksandra M
authors.initials: AM
authors.lastname: Walczak
authors.affiliation: Dipartimento di Fisica, Università Sapienza, Rome, Italy; Istituto Sistemi Complessi, Consiglio Nazionale delle Ricerche, UOS Sapienza, Rome, Italy.
authors.forename: Lorenzo Del
authors.initials: LD
authors.lastname: Castello
authors.affiliation: SUPA, Institute for Complex Systems and Mathematical Biology, Kings College, University of Aberdeen, Aberdeen, UK.
authors.forename: Francesco
authors.initials: F
authors.lastname: Ginelli
authors.affiliation: Dipartimento di Fisica, Università Sapienza, Rome, Italy; Istituto Sistemi Complessi, Consiglio Nazionale delle Ricerche, UOS Sapienza, Rome, Italy.
authors.forename: Stefania
authors.initials: S
authors.lastname: Melillo
authors.affiliation: Dipartimento di Informatica, Università Sapienza, Rome, Italy; Istituto Sistemi Complessi, Consiglio Nazionale delle Ricerche, UOS Sapienza, Rome, Italy.
authors.forename: Leonardo
authors.initials: L
authors.lastname: Parisi
authors.affiliation: Dipartimento di Fisica, Università Sapienza, Rome, Italy; Istituto Sistemi Complessi, Consiglio Nazionale delle Ricerche, UOS Sapienza, Rome, Italy.
authors.forename: Massimiliano
authors.initials: M
authors.lastname: Viale
authors.affiliation: Istituto Sistemi Complessi, Consiglio Nazionale delle Ricerche, UOS Sapienza, Rome, Italy.
authors.forename: Andrea
authors.initials: A
authors.lastname: Cavagna
authors.affiliation: Dipartimento di Fisica, Università Sapienza, Rome, Italy; Istituto Sistemi Complessi, Consiglio Nazionale delle Ricerche, UOS Sapienza, Rome, Italy.
authors.forename: Irene
authors.initials: I
authors.lastname: Giardina