Half the world's population owns roughly two percent of total wealth. This is usually discussed as a policy outcome — the result of tax structures, inheritance laws, market access, historical exploitation. The distribution is treated as contingent: different choices would produce different numbers.
Frahm and Shepelyansky (arXiv:2603.24190) show that the same distribution arises from the nonlinear chaotic dynamics of coupled oscillators with stratified energies. In their model, agents interact through a social network, energies play the role of wealth, and the system conserves total energy and probability norm. Above a chaos threshold, the dynamics drives the system toward a Rayleigh-Jeans distribution — the classical analog of Bose-Einstein statistics — where norm condenses at low-energy modes. The bottom half of the population accumulates only a small fraction of total wealth, not because of any designed mechanism but because the thermalized distribution concentrates probability at low energies.
The mathematical structure is identical to Bose-Einstein condensation in quantum gases, where below a critical temperature, a macroscopic fraction of particles occupies the ground state. In the social model, the “ground state” is the lowest wealth level, and condensation means a macroscopic fraction of the population accumulates there. The condensation is a phase transition — not a gradual drift but a sharp threshold above which inequality becomes structural.
This doesn't mean policy is irrelevant. It means policy operates against a thermodynamic baseline. The chaotic dynamics of interacting agents with stratified positions naturally produces extreme inequality, and any system that doesn't actively counteract this tendency will converge to it. The condensation is the default, not the exception.
The model also reveals turbulence: when energy is pumped into and absorbed from the system (analogous to economic growth and consumption), Kolmogorov-Zakharov cascades appear — wealth doesn't just condense at the bottom but flows through intermediate scales in a structured way. The inequality isn't static. It's dynamically maintained by the same nonlinear interactions that create it.