A thermodynamic state-space description of a monetary Schelling segregation model

Social segregation is a phenomenon that has been studied in sociological research. Migration patterns tend toward neighborhoods of similar identities. A well known and long established model for simulating the effect of such dynamics is the Schelling model of segregation known as multi-agent models. Throughout the literature many variants of this model have emerged. This paper builds on previous research by providing a thermodynamics-based approach. In this approach, we incorporate into the Schelling model two components monetary value and satisfaction which correspond to availability of funds and agent identity which is a surrogate for satisfaction. The introduction of funds and satisfaction do not hinder the core structure of the canonical version, while the results obtained add to existing scholarship. The key to this ability is the definition of quantities such as potential and kinetic energies derived from satisfaction and monetary funds components to model agent behavioral patterns. Furthermore, quantities such as entropy, heat, and the Helmholtz equation of state are appropriately and analogously defined. These thermodynamical quantities help parametrize and quantify stability properties as well as the influence of external factors on multi-agent systems providing a concise description. The overarching goal is to advance the techniques of Social physics with tools deriving from Thermodynamics. A thorough understanding of migration patterns (kinetics of movement in the context of milieu) can be understood by incorporating root causes into socio-physical models of migration which could inform decision makers to implement appropriate policies to tackle polarization.