The probability distribution of money among the agents in a closed economic system can be derived similarly to the probability distribution of energy among molecules in a gas, by treating economic transactions as collisions between molecules.
Analysis of empirical data shows that income distributions in the USA, European Union, and other countries exhibit a well-defined two-class structure. The majority of the population (about 97%) belongs to the lower class characterized by the exponential ("thermal") distribution, as in a gas. The upper class (about 3% of the population) is characterized by a power-law ("superthermal") distribution, and its share of the total income expands and contracts dramatically during booms and busts in financial markets.