Dynamical thermalization and turbulence in social stratification models

Battle Count: 55

This is a theoretical physics paper applying statistical mechanics and nonlinear dynamics to model social stratification and wealth inequality. While it touches on wealth distribution (Lorenz curves, Gini coefficients) and could tangentially inform macro-level economic modeling, it has essentially no direct relevance to quantitative trading strategies, market microstructure, algorithmic execution, or financial time series analysis. The wealth distribution modeling is at a societal/macro level, not at the asset pricing or trading signal level.

Implementation requires: (1) constructing the matrix H from Newman's collaboration network data with diagonal stratification and GOE perturbation, (2) diagonalizing H to obtain eigenmodes and eigenenergies, (3) implementing a symplectic 4th-order integrator for the nonlinear Schrödinger-type equation, (4) computing time-averaged mode probabilities, entropies, and IPR values, (5) solving the implicit equation for chemical potential mu(E), (6) constructing Lorenz curves and computing Gini coefficients, and (7) for the KZ turbulence case, implementing the modified dynamics with pumping/absorption terms. The physics background needed (Hamiltonian dynamics, RMT, wave turbulence) adds to the conceptual complexity.

The paper provides detailed model parameters (N=379, W=8, f=0.1, kappa=0.5, beta=2 and 4, gamma=sigma=0.01), specifies the exact network data source (Newman's collaboration network from refs [42-45]), describes the numerical method (symplectic 4th-order integrator), and states that supporting data is available within the article. However, no code repository is provided, and reproducing the full numerical results would require implementing the symplectic integrator and constructing the specific matrix H from the raw network data.