Nonequilibrium Thermodynamics of Wealth Condensation

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We analyze wealth condensation for a wide class of stochastic economy models on the basis of the economic analog of thermodynamic potentials, termed transfer potentials. The economy model is based on three common transfers modes of wealth: random transfer, profit proportional to wealth and motivation of poor agents to work harder. The economies never reach steady state. Wealth condensation is the result of stochastic tunneling through a metastable transfer potential. In accordance with reality, both wealth and income distribution transiently show Pareto tails for high income subjects. For metastable transfer potentials, exponential wealth condensation is a robust feature. For example with 10 % annual profit 1% of the population owns 50 % of the wealth after 50 years. The time to reach such a strong wealth condensation is a hyperbolic function of the annual profit rate.