Mutual Information Reveals Emergent Effects of Self-Avoidant Memory in Curvature Statistics of Particle Paths.

Chemically induced swimming of microdroplets motivates a model for self-avoidant particles which exhibit novel trajectory statistics at long timescales. As the particles stochastically explore the self-generated and time-evolving concentration field, they often turn in on their own past history and create concentration "traps" which arrest the overall displacement for a period of time. This transient self-trapping is revealed in the path data as areas of extremely high correlated curvature and it is expressed statistically as suppressed enhanced diffusion when compared to traditional active particle models. We explore the shortcomings of traditional models in explaining this behavior and suggest mutual information as an additional tool can be used to quantify this emergent effect.