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

Author:

Fu Yulei1ORCID,Wu Zongyuan12ORCID,Zhan Sirui13,Yang Jiacheng4,Gardi Gaurav56,Kishore Vimal7ORCID,Malgaretti Paolo8,Wang Wendong1ORCID

Affiliation:

1. University of Michigan—Shanghai Jiao Tong University Joint Institute, Shanghai Jiao Tong University, Shanghai 200240, China

2. Department of Mechanical Engineering, Carnegie Mellon University, 5000 Forbes Ave, Pittsburgh, PA 15213, USA

3. College of Engineering, University of Michigan, Ann Arbor, MI 48109, USA

4. The Academy for Engineering and Technology, Fudan University, Shanghai 200433, China

5. Physical Intelligence Department, Max Planck Institute for Intelligent Systems, 70569 Stuttgart, Germany

6. Department of Physics, University of Stuttgart, 70569 Stuttgart, Germany

7. Department of Physics, Banaras Hindu University, Varanasi 221005, India

8. Helmholtz Institute Erlangen-Nürnberg for Renewable Energy (IEK-11), Forschungszentrum Jülich, 52425 Jülich, Germany

Abstract

Collective systems self-organize to form globally ordered spatiotemporal patterns. Finding appropriate measures to characterize the order in these patterns will contribute to our understanding of the principles of self-organization in all collective systems. Here we examine a new measure based on the entropy of the neighbor distance distributions in the characterization of collective patterns. We study three types of systems: a simulated self-propelled boid system, two active colloidal systems, and one centimeter-scale robotic swarm system. In all these systems, the new measure proves sensitive in revealing active phase transitions and in distinguishing steady states. We envision that the entropy by neighbor distance could be useful for characterizing biological swarms such as bird flocks and for designing robotic swarms.

Funder

Science and Technology Commission of Shanghai Municipality

UM-SJTU JI

SERB India

IoE BHU

Publisher

MDPI AG

Subject

Electrical and Electronic Engineering,Mechanical Engineering,Control and Systems Engineering

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