Connect nonlinear oscillators through a social network graph, let them exchange energy, and add stratification — the tendency for high-energy oscillators to preferentially connect with other high-energy oscillators. What distribution of energy emerges?
Frahm and Shepelyansky (arXiv: 2603.24190) show it's a Rayleigh-Jeans distribution with condensation. Above a chaos threshold, the oscillator energies thermalize. But the thermalized distribution is not uniform — it condenses at the low-energy modes. Most of the “norm” (the conserved quantity analogous to total wealth) concentrates in a few high-energy oscillators, while the majority of oscillators hold negligible energy.
The parallel to real wealth distribution is structural: approximately half the global population controls a tiny fraction of total wealth, not because of any particular policy or historical accident, but because this is what thermalization on stratified networks produces. The condensation is a statistical mechanical inevitability, not a social failure. With energy input and dissipation, the system develops Kolmogorov-Zakharov turbulence — the wealth distribution fluctuates with the same statistics as turbulent energy cascades.
The through-claim: inequality is a condensation phenomenon. In a system of interacting agents on a stratified network, the Rayleigh-Jeans equilibrium naturally concentrates resources at one end of the spectrum. The condensation doesn't require greed, exploitation, or market failure. It requires only nonlinear interaction, network structure, and conservation. The troubling implication: if inequality is thermodynamic, reducing it requires continuously pumping against equilibrium.
Frahm & Shepelyansky, 2603.24190. Statistical mechanics / network dynamics / wealth distribution / turbulence.