Nonequilibrium Thermodynamics of Wealth Condensation

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. Introduction. Modelling Economies focusses on deterministic agents in equilibrium. From the viewpoint of statistical mechanics, two essentials are missing: randomness and non-equilibrium dynamics. Randomness since agents decide from a chaotic, subjective environment. Since economies are built from exchange and credit relations between people and therefore between living disequilibrium entities, approaches far from equilibrium should be seriously pursued. Even if a steady state can be reached in principle, settling times are probably more on the order of years than days with persistent drifts in state variables.