Influence and information in a collective of self-propelled particles

While information-theoretic quantities, such as transfer entropy, have been widely adopted to infer causal relationships in collective systems, a critical gap exists: the absence of quantitative evidence directly linking information-theoretic quantities to a physically defined influence. This letter addresses this gap by proposing a modified Vicsek model that enables the calculation of a physically interpretable influence grounded in the angular interactions between particles. Averaged pairwise influences can serve as new order parameters to indicate collective phase transitions. We reveal quantitative relations between information, represented by transfer entropy, and average influence in pairwise and collective interactions. We test three typical methods of partial information decomposition and find that the method based on intrinsic mutual information gives the most appropriate interpretation. Overall, this work provides a model system for quantitative studies of influence and information in complex systems.