Time evolution of neighbor-pair mutual information in collectively moving active granular particles

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In recent decades, significant progress has been made in the field of active-matter research. Studies on biological active systems, in particular, have begun to adapt information-theoretic approaches in studying collective behavior in various systems. In this present work, we employ a novel information-theoretic framework based on connected mutual information (CMI) to quantify the similarities in the speed and polarization fluctuations among individuals in a system of 10–100 bio-inspired, vibrated active granular particles. By tracking the evolution of the speed and polarization CMI using 20-s time windows, we find that CMI estimates rise and fall over a 3-min observation period depending on the number of particles and the system's overall mobility. Results of nonlinear analyses also reveal that the speed and polarization fluctuations are independent of each other, and that the sharing of speed and polarization information among active particles is maximized when the system is continuously circulating around the container, and minimized when the system is either jammed or is executing frequent directional switches from clockwise to counter-clockwise circulation and vice versa. The information-theoretic methodologies presented in this work can have potential applications in the study of different biological and artificial active systems.