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The first statistics program written, calcTemp, was written to look at the kinetic energy distribution, and produce a plot of the distribution of kinetic energy. It was expected that the kinetic energy distribution would rapidly approach a Maxwellian distribution. The plot would also serve to diagnose the random initial distribution function that was, at the time, about to written.
A plot of total kinetic energy, as a function of time is shown in plot 1. It can be seen that the total kinetic energy appears to increase over time. An extension of the plot (plot 2) to a longer time period demonstrates that the this is not merely an initial adjustment period. The data was produced by a simulation using the greedy algorithm. It should be clear that a pairing strategy that doesn't move smoothly from one pairing to another will cause jumps in the potential energy function. An increase in potential energy will produce an added force, which will tend to increase the kinetic energy.
Plot 3 shows a plot of both kinetic and potential energy for the stable marriage pairing algorithm. Unfortunately, the two energies are on different scales, so the third plot, their sum, is somewhat meaningless.
Closer examination of the potential energy plot reveals that the points appear to be oscillating at a period close to the sampling period. In order for energy to be conserved, the kinetic energy should also be observed to oscillate. It is possible that the kinetic energy plot also oscillates at another scale. This has not really been observed, likely due to rounding of the data.
The important point, however, is that the kinetic energy plot appears to increase slowly, while an average line through the potential energy plot stays approximately horizontal.