Kac Ring Model

N sites on a ring, M marked bonds. Particles advance and flip at marked bonds.
Illustrates Boltzmann's H-theorem, Poincaré recurrence, and the reversibility paradox.

Parameters

Sites N: 60 Marked bonds M: 10 Initial +1 fraction: 0.80 Speed: 2 steps/frame

Step: 0

Magnetization: —

Recurrence period: —

Kac 1959: Exact model showing:
• Approach to equilibrium (M=0)
• Poincaré recurrence at t=2N
• Time-reversal restores order
• "Irreversibility" is statistical

Period = 2N (exact recurrence)
M marked bonds → entropy rises
only on average, not always.