Vicsek Model by Time-Interlaced Compression: a Dynamical Computable Information Density

TL;DR

This paper demonstrates that a compression-based entropy measure, the Computable Information Density (CID), effectively distinguishes phases in the Vicsek model of collective motion, especially when incorporating a novel space-time encoding scheme.

Contribution

The study introduces a new space-time locality-preserving encoding method for CID, enhancing phase detection in out-of-equilibrium systems like the Vicsek model.

Findings

CID distinguishes noise regimes and phase transitions.

Space-time encoding reduces CID, improving data robustness.

Method is effective with partial or corrupted data.

Abstract

Collective behavior, both in real biological systems as well as in theoretical models, often displays a rich combination of different kinds of order. A clear-cut and unique definition of "phase" based on the standard concept of order parameter may therefore be complicated, and made even trickier by the lack of thermodynamic equilibrium. Compression-based entropies have been proved useful in recent years in describing the different phases of out-of-equilibrium systems. Here, we investigate the performance of a compression-based entropy, namely the Computable Information Density (CID), within the Vicsek model of collective motion. Our entropy is defined through a crude coarse-graining of the particle positions, in which the key role of velocities in the model only enters indirectly through the velocity-density coupling. We discover that such entropy is a valid tool in distinguishing the various noise regimes, including the crossover between an aligned and misaligned phase of the velocities, despite the fact that velocities are not used by this entropy. Furthermore, we unveil the subtle role of the time coordinate, unexplored in previous studies on the CID: a new encoding recipe, where space and time locality are both preserved on the same ground, is demonstrated to reduce the CID. Such an improvement is particularly significant when working with partial and/or corrupted data, as it is often the case in real biological experiments.