Memory signatures in path curvature of self-avoidant model particles are revealed by time delayed self mutual information

Emergent behavior in active systems is a complex byproduct of local, often pairwise, interactions. One such interaction is self-avoidance, which experimentally can arise as a response to self-generated environmental signals; such experiments have inspired non-Markovian mathematical models. In previous work, we set out to find “hallmarks of self-avoidant memory" in a particle model for environmentally responsive swimming droplets. In our analysis, we found that transient self-trapping was a spatial hallmark of the particle’s self-avoidant memory response. The self-trapping results from the combined effects of behaviors at multiple scales: random reorientations, which occur on the diffusion scale, and the self-avoidant memory response, which occurs on the ballistic (and longer) timescales. In this work, we use the path curvature as it encodes the self-trapping response to estimate an “effective memory lifetime" by analyzing the decay of its time-delayed mutual information and subsequently determining the longevity of significant nonlinear correlations. This effective memory lifetime (EML) is longer in systems where the curvature is a product of both self-avoidance and random reorientations as compared to systems without self-avoidance.Author summary: How individual agents such as fish or bacteria interact with each other and their environments to create emergent complex behavior remains an active area of research. In experiments, often only the trajectory of the agents can be measured directly, rather than the forces that combine to create this movement. In this work, we present a method for detecting “hallmarks of self-avoidant memory” from trajectory data for a synthetic environmentally responsive swimming droplet. Because these droplets swim fast relative to the speed at which diffusion erases their self-created chemical gradients, they avoid each other’s and their own past locations. Our method quantifies the effect of this effective memory of past locations on the movement of the droplets, estimating a effective memory lifetime.