Entropy by Neighbor Distance as a New Measure for Characterizing Spatiotemporal Orders in Microscopic Collective...

Area of Science:

• Collective behavior
• Complex systems
• Statistical physics

Background:

• Collective systems exhibit self-organization into ordered spatiotemporal patterns.
• Understanding self-organization principles requires robust measures of pattern order.

Purpose of the Study:

• To introduce and evaluate a novel measure for characterizing order in collective systems.
• To assess the measure's sensitivity in identifying phase transitions and steady states.

Main Methods:

• Utilized a novel measure based on the entropy of neighbor distance distributions.
• Applied the measure to diverse systems: simulated boids, active colloids, and robotic swarms.

Main Results:

• The entropy-based measure effectively characterized order across all studied systems.
• The measure demonstrated sensitivity in detecting active phase transitions.
• The measure successfully distinguished between different steady states in collective patterns.

Conclusions:

• Entropy by neighbor distance is a valuable tool for analyzing collective pattern order.
• This measure can aid in understanding biological swarms like bird flocks.
• The measure has potential applications in the design of robotic swarms.