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## Temperature

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.

*mcr@ccs.carleton.ca*