Spectral Concentration in Disordered Non-Equilibrium Systems: A Low-Variance Order Parameter for the Edge of Chaos

Dynamical phase transitions in systems with quenched random interactions exhibit critical behavior analogous to equilibrium statistical mechanics, yet conventional order parameters suffer from divergent variance in finite-size realizations. We demonstrate that the spectral concentration index—originally developed for quantum entanglement detection—provides a robust diagnostic when applied to temporal covariance matrices of classical stochastic trajectories. Numerical simulations of N=500 coupled nonlinear degrees of freedom with asymmetric Gaussian couplings reveal a sharp transition at critical gain g_c ≈ 1.0, separating a low-dimensional ordered phase from high-dimensional chaotic dynamics. The concentration metric K_c = Σp_i² (where p_i are normalized covariance eigenvalues) exhibits coefficient of variation one order of magnitude smaller than von Neumann entropy in the ordered regime, while the susceptibility χ = |dK_c/dg| peaks with 17-fold enhancement at criticality. These results extend quantum-inspired concentration frameworks to classical many-body systems, demonstrating universal applicability across localization phenomena in both quantum and classical domains.