Money: In a closed economic system, money is conserved. Thus, by analogy with energy, the equilibrium probability distribution of money must follow the exponential Boltzmann-Gibbs law characterized by an effective temperature equal to the average amount of money per economic agent. We demonstrate how the Boltzmann-Gibbs distribution emerges in computer simulations of economic models. Then we consider a thermal machine, in which the difference of temperatures allows one to extract a monetary profit. We also discuss the role of debt, and models with broken time-reversal symmetry for which the Boltzmann-Gibbs law does not hold.
Income: Using tax and census data, we demonstrate that the distribution of individual income in the United States is exponential. Our calculated Lorenz curve without fitting parameters and Gini coefficient 1/2 agree well with the data. From the individual income distribution, we derive the distribution function of income for families with two earners and show that it also agrees well with the data. The family data for the period 1947-1994 fit the Lorenz curve and Gini coefficient 3/8=0.375 calculated for two-earners families.