Learning Maximum Entropy Probability Distributions for the Vicsek Model and Motile E .coli Bacteria Surrounding an Information "Black Hole"

Abstract

Previous literature shows that observed flocks of birds have directional correlations that can be described by a maximum entropy probability distribution that is shared with a Heisenberg Spin model or in two dimensions, an XY model. However, this paper shows that the two dimensional Vicsek model lacks this property. First, background on the XY model and Vicsek model is provided. Next, machine learning algorithms are used to try and find a maximum entropy probability distribution for Vicsek correlations. However, the strange, competing behavior of learned couplings in the XY model indicate that an equilibrium probability distribution cannot describe the Vicsek model. Finally, a two dimensional system of E. coli bacteria is studied and it is found that directional correlations cannot be described by a maximum entropy probability distribution.