The opinion dynamics studies how a final consensus emerges from a diversified initial configuration. The final result can be an artifact arising in the voting processes and overlook the features of the initial configuration, which leads to the unfair result. We explore the concept of fairness in...

Three different types of inversion temperatures are discussed. Their relationships to the second virial coefficient are explored with the intermolecular interactions. A modified hard-sphere system is introduced to present these phenomena with elementary calculus.