© 2026 Theodore P. Pavlic & Greg T. Chism · MIT License

Boltzmann Distribution via Random Exchange

N agents trade random wealth — any initial distribution converges to the maximum-entropy Boltzmann (exponential) equilibrium  P(w) = (1/μ) e−w/μ


Click to choose an initial wealth distribution:
Equal (δ-function at μ). Every agent begins with exactly the same wealth W/N — maximum order, minimum entropy. Watch it broaden into the exponential. The system spontaneously generates inequality from a perfectly egalitarian start.
Wealth Distribution
Sweeps
0
N trades each
Empirical Mean
Theoretical μ
Wtotal / N
Fit to Exp(μ)
Agents N
Speed 2 sweeps / frame