The light blue square is 300x300 pixels - 90,000 pixels total. Each pixel can exist
in one of two states, light blue, or dark blue (the dark blue square is just the dual
of the light blue). Each time cycle a single pixel will switch states. Once the square
has changed from its initial state (all pixels light blue - very low probability state),
it is virtually impossible that it will ever spontaneously revert. Most states are
in the roughly 50-50 region (ie., 50% light blue, and 50% dark). These high probability
states have the highest entropy.
It is not surprising that entropy changes are largest when the system is in a low probability
state. This is somewhat analogous to adding heat (Q) to an ideal gas kept at a constant
volume. Adding heat raises the temperature. At any given moment the increase in entropy, dS,
due to added heat, dQ, is dS = dQ/T. So (dS/dt) = (dQ/dt)/T. If the rate that heat is
added (dQ/dt) is a constant, then the rate of entropy increase (dS/dt) is highest when
T is smallest. At constant volume, dQ/T is proportional to dQ/Q, the fractional increase
in heat, which is in a sense the fractional increase in gas aggitation (kinetic energy).
Likewise, the difference of one state (above) to the next is most marked when the initial state
has a low probability, the anolog of temperature in this case. The analog of added heat
is just the random change of one pixel's state per cycle. Probability drives the system
to ever increasing states of agitation, ending for this finite system when both squares
have roughly equal numbers of on and off pixels. (June 2003)