Collective behaviors in regional seismic responses: insights from phase transitions in statistical physics

Regional seismic risk assessments are typically performed through bottom-up approaches.This approach provides high-resolution responses but often overlooks macroscopic patterns underlying the regional behavior.Moreover, modeling uncertainties and their compounded effects, as well as the interdependencies between hazard and structural performance, further complicate the identification of emergent collective behaviors.We propose a complementary top-down perspective that characterizes regional-scale seismic behavior using concepts from statistical physics.Within a probabilistic simulation framework, we augment conventional models by introducing an additional epistemic uncertainty term to represent model incompleteness.Applying the framework to the residential building portfolio in Milpitas, California, comprising 13,049 buildings, we construct a phase diagram that summarizes regional seismic behavior in a hazard-uncertainty space, with earthquake magnitude and epistemic uncertainty as coordinate axes.Two main findings emerge: (1) a discontinuous phase transition, representing an abrupt shift from a collective safe state to a collective failure state, occurs as the magnitude exceeds a critical threshold; and (2) a continuous phase transition, where the statistical distribution of system-level losses evolves smoothly from a bimodal to a unimodal distribution as epistemic uncertainty grows.Mapping these findings onto a classical statistical physics model clarifies how correlation, heterogeneity, and uncertainty govern systemic fragility: correlations buffer minor hazards but trigger a 'brittle systemic collapse' under larger events; structural diversity enhances 'global ductility'; and excessive epistemic uncertainty blurs the phase boundary, potentially leading to a misrepresentation of regional seismic risk.This study advances a high-level understanding of regional seismic risk by revealing collective behaviors and phase transitions, complementing detailed bottom-up simulations and informing system-level resilience strategies.