Statistical mechanics of money

Abstract. 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 eective 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 dierence of temperatures allows one to extract a monetary prot. We also discuss the role of debt, and models with broken time-reversal symmetry for which the Boltzmann-Gibbs law does not hold. The instantaneous distribution of money among the agents of a system should not be confused with the distribution of wealth. The latter also includes material wealth, which is not conserved, and thus may have a dierent (e.g. power-law) distribution. PACS. 87.23.Ge Dynamics of social systems { 05.90.+m Other topics in statistical physics, thermodynamics, and nonlinear dynamical systems { 89.90.+n Other topics of general interest to physicists { 02.50.-r Probability theory, stochastic processes, and statistics