Towards a Framework for Social Mechanics

Abstract

Social physics explores the possibility that mathematical structures developed in physics may provide useful descriptions of certain social phenomena. In this work, we propose an effective mechanical framework for modelling social change in terms of positions in a space of social stances, together with concepts analogous to motion, inertia, interaction, and force. A central feature of the framework is the introduction of position-dependent inertial responses, allowing susceptibility to social change to vary across stance-space. Within this setting, we investigate deterministic and stochastic models of social evolution, including free motion, effective interactions, and diffusion-driven dynamics. We also discuss Lagrangian and Hamiltonian formulations associated with the proposed framework. As an illustrative application, we model partisan preference distributions in United States presidential elections through effective drift and diffusion processes. The framework is intended as a phenomenological and exploratory approach to social dynamics rather than as a fundamental description of human behaviour.