Gas-like economic exchanges — Maxwell-Boltzmann statistics emerge from random trades
The kinetic exchange model (Dragulescu & Yakovenko 2000) treats wealth like energy in an ideal gas. Agents randomly trade random fractions of their combined wealth. Despite the simplistic rules, the equilibrium wealth distribution converges to the Boltzmann-Gibbs exponential distribution P(w) ∝ e−w/⟨w⟩ — exactly as in statistical mechanics. Most agents become poor; a few become very rich, not through skill but pure statistical fluctuation. A wealth floor (minimum income) shifts the distribution and reduces inequality; taxation + redistribution can flatten it further.
econophysicsBoltzmanninequalitykinetic exchange