Abstract: Inequality is an important and seemingly inevitable aspect of the human society.  Various manifestations of inequality can be derived from the concept of entropy in statistical physics.  In a stylized model of monetary economy, with a constrained money supply implicitly reflecting constrained resources, the probability distribution of money among the agents converges to the exponential Boltzmann-Gibbs law due to entropy maximization.  Our empirical data analysis shows that income distributions in the USA, European Union, and other countries exhibit a well-defined two-class structu