A General Statistical Mechanics Framework for the Collective Motion of Animals

We propose a general statistical mechanics framework for the collective motion of animals. The framework considers the principle of maximum entropy, the interaction, boundary, and desire effects, as well as the time-delay effect. These factors provide the ability to describe and solve dynamic and non-equilibrium problems under this framework. We show that the Vicsek model, the social force model, and some of their variants can be considered special cases of this framework. Furthermore, this framework can be extended to the maximum caliber setting. We demonstrate the potential of this framework for model comparisons and parameter estimations by applying the model to observed data from a field study of the emergent behavior of termites. Finally, we demonstrate the flexibility of the framework by simulating some collective moving phenomena for birds and ants.