Mutual Information as a Tool for Identifying Phase Transitions in Dynamical Complex Systems With Limited Data
arXiv:physics/0612198 · doi:10.1103/PhysRevE.75.051125
Abstract
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.
7 pages, 11 figures
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