Personal income distribution in the USA has a well-defined two-class structure. For the lower class, to which the majority of population (97-99%) belongs, income distribution is the characterized by the exponential law. For the upper class (1-3% of population), income distribution follows the Pareto power law. In the presented paper [1], we performed quantitative computer analysis of the income distribution data in the USA for 1983-2001 obtained from the Internal Revenue Service. We found that the exponential income distribution for the lower class is essentially stationary in time, save for a gradual increase of the average income in nominal dollars with inflation. On the other hand, the power-law tail swells and shrinks following the stock market. In the last 20 years, the total income in the power-law tail increased by a factor of 5, but then started to decline after collapse of the US stock market. We argue that the stationary exponential distribution, characterizing the majority of population, is analogous to the well-known exponential Boltzmann-Gibbs distribution of energy in physics in statistical thermal equilibrium at a given temperature. Statistical mechanics and economics have many things in common, because they both describe big statistical ensembles of objects or agents [2]. It is well known that the exponential Boltzmann-Gibbs distribution maximizes entropy and, thus, is stable with respect to the second law of thermodynamics. Using this analogy, we discuss the concept of equilibrium inequality in a society, based on the principle of maximal entropy. By doing computer analysis of the time evolution of the Lorenz curves and the Gini coefficient in 1983-2001, we quantitatively show that the concept of equilibrium inequality indeed applies to the majority of population. At the same time, the upper tail of income distribution is clearly out of thermal equilibrium, following power law and changing significantly in time. It is analogous to the so-called “superthermal†tail known in physics of non-equilibrium systems. We hope that this new perspective from the point of view of statistical physics and computer analysis of modern statistical data would bring new fresh insight into the old questions about probability distributions of money, income, and wealth in a society and their inequality. [1] A. C. Silva and V. M. Yakovenko, "Temporal evolution of the `thermal' and `superthermal' income classes in the USA during 1983-2001", Europhysics Letters, v. 69, pp. 304-310 (2005). [2] A. A. Dragulescu and V. M. Yakovenko, "Statistical mechanics of money", The European Physical Journal B, v. 17, pp. 723-729 (2000)
