Boltzmann's Roulette:
(The savants call it "Method of the most probable distribution")

For the hard discs system, mu-space - or rather, mu-plane - is spanned by vx,vy; the state of the system is represented by a swarm of N points on that plane.

To find the average (and also most probable!) distribution of particle energies Boltzmann suggested the following game:
  • Throw N particles randomly onto equal-sized cells on the mu-plane
  • Make sure that the sum of the particle energies equals the given system energy
  • Determine the mean number of particles in each cell on the mu-plane; sort the result according to the cell energies
To this date, this game has never actually been played; rather, its outcome was calculated as seen in the textbooks.

[Code: LBRoulette]

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