  As social behavior plays an essential role in people's lives, the features of
face-to-face interaction networks must be examined to understand people's
social behavior. In this study, we focused on the stable community structure of
a face-to-face interaction network because it explains the persistent
communities caused by the stationary communication patterns of citizens and
visitors in a city. We regarded citizens and visitors as two kinds of particles
and the community as a phase and theorized the stability of the community
structure using the equilibrium conditions among communities. We formulated the
chemical potentials of the communities and examined whether they were in
equilibrium under the assumption of a canonical ensemble. We estimated the
chemical potentials of persistent communities and found that these values
matched within approximately 10% error for each day. This result indicates that
the cause of persistent communities is the stability of community structure.
