Urban-scale structural systems composed of many buildings are commonly modeled as collections of weakly interacting nonlinear oscillators. While linear superposition is often assumed, even weak inter-building coupling can fundamentally alter the global response. In such regimes, collective dynamics emerge that cannot be reduced to individual behavior, including coherent frequency shifts and long-range phase organization observed at the city scale [1, 2]. To capture these effects, we introduce a reduced envelope-based description that separates slow collective dynamics from fast linear oscillations. By averaging over rapid phases, the original equations of motion are transformed into effective envelope equations governed solely by mechanical parameters. This reduction circumvents the computational limitations of direct numerical simulation and reveals latent macroscopic degrees of freedom governing collective behavior. In the large-box limit, nonlinear interactions manifest through an infinite set of resonant channels in Fourier space. Although individual interaction pathways are intractable, their cumulative effect produces a statistically regular evolution of modal amplitudes on slow time scales. The resulting dynamics are well-approximated by effective stochastic processes, leading to a stationary modal energy distribution [3]. We show that this distribution converges to a Rayleigh–Jeans distribution, indicating ergodic behavior with vanishing fluctuations at large scales. Within this framework, a thermodynamic interpretation naturally emerges. An effective temperature is defined directly from the modal energy distribution and expressed entirely in terms of mechanical system parameters. This establishes a direct correspondence between microscopic structural properties and macroscopic collective observables, analogous to Boltzmann statistical thermodynamics. The proposed formulation provides a unified theoretical basis for predicting and controlling emergent phenomena in large-scale structural systems, including phase transitions in distance-dependent correlations.