Thermodynamic framework for modeling social adoption in multi-agent systems

We develop a thermodynamic framework for modeling innovation adoption and abandonment dynamics using statistical mechanics. Starting from a mathematical model for an adoption distribution that fits empirically obtained date, we construct a canonical ensemble whose equilibrium distribution yields Gompertz-like and Maxwell-Boltzmann-like shapes. By reverse-engineering the associated energy landscape, we define an effective potential and derive a dynamical Lagrangian formulation. The resulting field theory captures key features of emergent behaviors in sociotechnical systems, from early suppression to peak dynamics and late decline. We interpret effective temperature, entropy, and equilibrium points and show how these systems exhibit hybrid thermodynamic-statistical signatures.