In the final film, the starting position is the end point of the previous HOT and COLD boards. The histogram for the HOT board has Ratio R=2 between columns for a board with 900 energy units (quanta) and 900 atoms. The board to the right is the COLD board which has a ratio R=4 for a board with 300 quanta and 900 atoms. The two boards are then brought together and moves may now take place between atoms on either board. As the animation runs, quanta gradually move from the hot board to the cold board until an equal number of quanta appear on each board. The histograms for each board move from their initial distributions to the same distribution having a ratio R = 2.5 between columns.

The exchange of energy between these boards is a model of heat flow. The temperatures of the two boards have become equal. Heat flow from hot to cold has been demonstrated. This may look like an obvious result which does not require this amount of effort. However the important point is that this flow came about by random shuffling. Heat flow occurred spontaneously by chance.

Move = 0 COMBINED COLD COLD HOT HOT