Stochastic Dynamics of Social Change: Regularity, Contingency, and the Arrow of Time
ABSTRACT
How can we distinguish regularity from contingency in social change, and identify when realized trajectories become atypical or exhibit a statistical arrow of time? We address this problem by inferring stochastic dynamics from observed social trajectories using stochastic differential equations (SDEs), with the drift term capturing conditional tendencies and the diffusion term capturing state-dependent stochastic variability. Applying this framework across three social domains---modern political economy, quantitative history, and cultural analytics---we use the inferred SDEs as probabilistic reference dynamics and evaluate individual observed trajectories against the trajectory distributions implied by these dynamics. Across these domains, the inferred SDEs reveal state-dependent organization of political-economic dynamics, a broad but stochastic tendency toward increasing social complexity in historical societies, and time-dependent reorganization of lexical dynamics. Relative to these reference dynamics, we identify statistically atypical transitions and characterize their temporal footprints. We further quantify temporal irreversibility, revealing persistent but heterogeneous directional asymmetries that need not coincide with transition atypicality. The framework thereby distinguishes reference dynamics, atypical transitions, and temporal directionality, providing a probabilistic basis for relating general patterns of social change to realized historical variation.
