Emergência e leis de escala em sistemas complexos: uma abordagem orientada por dados

Abstract

In this work, we investigate two complex systems of distinct natures under a single data-driven approach: (i) viscoelastic networks immersed in a fluid and (ii) the urban–economic system of Ceará, structured by multilayer trade flows among 184 municipalities. In both cases, we deal with many interacting elements, structural heterogeneity, and multiscale coupling, seeking to infer emergent macroscopic properties from high-dimensional local data through collective descriptors. In the viscoelastic study, we consider a model of an elastic network with sublinear dissipation, characterized by the parameter α ∈ [0,1] in the drag force fa = γvα. In homogeneous and rigid networks, the drag exponent α governs the transition between different relaxation regimes: within a specific sublinear range of α, the force response takes the form of a power law, F(t) ∼ t−β, whereas outside this range, exponential-type relaxation responses become predominant. In heterogeneous Gaussian networks, disorder broadens the range of α values that give rise to power-law relaxations, while preserving a robust interval of β values, which are mainly sensitive to the mean stiffness level and only weakly dependent on the width of its distribution. In the urban–economic system, we analyze more than 2.5 billion formal transactions (electronic invoices, NF-e, 2016–2019) and show that purchases, sales, and internal trade scale superlinearly with population, with distinct exponents. The economic indicator RCA (Revealed Comparative Advantage), used to characterize patterns of regional productive specialization, follows Zipf–Mandelbrot-type distributions for the three flow layers, revealing hierarchies and diversification limits. Municipal Fitness, an economic metric that measures the degree of diversification and productive complexity of cities based on their export products, also scales superlinearly, indicating a disproportionate accumulation of structural capabilities, especially on the supply side and in internal recirculation. The integration of these results shows that power laws, collective emergence, hierarchies, critical transitions, and multiscale organization are recurrent patterns in both viscoelastic materials and urban systems. We demonstrate that the combination of numerical simulations, machine learning, network analysis, Bayesian inference, and multivariate techniques consolidates Data Science as a unified framework for unveiling deep structures in seemingly disparate complex systems.