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Vicsek model by time-interlaced compression: A dynamical computable information density.

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This study shows computable information density effectively identifies phases in collective motion models. It distinguishes noise regimes and velocity alignment without directly using velocity data.

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Area of Science:

  • Physics
  • Complex Systems
  • Statistical Mechanics

Background:

  • Collective behavior in biological systems and models exhibits complex order.
  • Defining phases in non-equilibrium systems is challenging due to lack of thermodynamic equilibrium.
  • Compression-based entropies offer a promising approach for characterizing out-of-equilibrium systems.

Purpose of the Study:

  • To evaluate the effectiveness of computable information density as a compression-based entropy measure.
  • To analyze its performance in distinguishing phases within the Vicsek model of collective motion.
  • To explore the influence of spatial and temporal encoding on phase detection.

Main Methods:

  • Applied computable information density, a compression-based entropy, to the Vicsek model.
  • Defined the measure via coarse-graining particle positions, with indirect velocity influence through velocity-density coupling.
  • Developed an encoding recipe incorporating the time coordinate to preserve space-time locality.

Main Results:

  • Computable information density successfully distinguished various noise regimes in the Vicsek model.
  • The entropy measure identified the crossover between aligned and misaligned velocity phases without explicit velocity input.
  • Incorporating the time coordinate enhanced the detection signal, preserving space-time locality.

Conclusions:

  • Computable information density is a robust tool for characterizing phases in non-equilibrium collective motion.
  • The method's ability to detect phase transitions without explicit velocity data is significant.
  • The inclusion of temporal information improves signal detection, beneficial for real-world, potentially noisy biological data.