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 is available, mutual information provides a better measure of the phase transition location than the susceptibility of the data.