Mutual Information as a Tool for Identifying Phase Transitions in Dynamical Complex Systems With Limited Data

We use a well known model (T. Vicsek et al. Phys Rev Lett 15, 1226 (1995)) for flocking to test mutual information as a tool for detecting order-disorder transitions, in particular when observations of the system are limited. We show that mutual information is a sensitive indicator of the phase transition location, in terms of the natural dimensionless parameters of the system which we have identified. When only a few particles are tracked, and when only a subset of the positional and velocity components are available, mutual information provides a better measure of the phase transition location than the susceptibility of the data.