N agents repeatedly trade random amounts of wealth. Total wealth W is strictly conserved.
The maximum-entropy equilibrium for any conserved non-negative quantity is
P(w) = (1/μ) e−w/μ
— regardless of initial conditions.
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.