Mutual information as function of separation distance between particles in vibrated active granular systems

Abstract

Studies have shown that self-propelled granular assemblies can mimic some of the collective behaviors typically observed in living systems. The use of information-theoretic approaches in studying both artificial and biological active systems has also gained traction in recent years. In this work, we examine the pairwise mutual information between particles (with respect to their speed, polarization, speed fluctuation, and polarization fluctuation time series) and its dependence on the separation distance r_AB between particles and the area fraction ϕ_AGP. We find that at low ϕ_AGP where particles move rather freely, mutual information rises with increasing r_AB. However, as more particles are added to the system at fixed container size, the sharing of motion-related information is amplified with decreasing r_AB, at a rate that is largely influenced by ϕ_AGP.