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We propose a general statistical mechanics framework for the collectivemotion of animals. The framework considers the principle of maximum entropy,the interaction, boundary, and desire effects, as well as the time-delayeffect. These factors provide the ability to describe and solve dynamic andnon-equilibrium problems under this framework. We show that the Vicsek model,the social force model, and some of their variants can be considered specialcases of this framework. Furthermore, this framework can be extended to themaximum caliber setting. We demonstrate the potential of this framework formodel comparisons and parameter estimations by applying the model to observeddata from a field study of the emergent behavior of termites. Finally, wedemonstrate the flexibility of the framework by simulating some collectivemoving phenomena for birds and ants.

A General Statistical Mechanics Framework for the Collective Motion of Animals