Ideal Social Gas: Emergent Thermodynamic Observables in an Effective Model of Social Dynamics

Abstract

This work continues the one commenced in \cite{m24}, where the key idea is that individual stances on a social matter can be modeled as positions of particles in physics. Here, we develop an effective thermodynamic framework for the statistical description of collective social systems based on a mechanical representation of individual stances. In this approach, each individual is modeled as a point-like particle evolving in an abstract stance-space, where the dynamics are characterized by position-dependent inertial response functions. The resulting many-particle system is treated within an equilibrium statistical description analogous to the canonical ensemble of statistical mechanics. Using this framework, we derive the corresponding partition function and introduce emergent macroscopic observables analogous to pressure, volume and temperature, interpreted here as collective statistical properties of the social system. For a particular class of position-dependent mass functions, the resulting equation of state acquires an ideal-gas-like form, suggesting a degree of macroscopic universality despite microscopic heterogeneity among individuals. The formalism is further extended to open social systems through the introduction of a chemical potential associated with population exchange among social groups. This extension naturally allows the treatment of variable particle number and multispecies social configurations within the same equilibrium framework. The present work is intended as an exploratory phenomenological contribution to sociophysics and complex systems research, aimed at investigating whether collective social behavior may admit effective macroscopic statistical descriptions analogous to those encountered in statistical physics.