The Misunderstood Nature of Entropy episode of the PBS “Space Time” series uses a go board as a nice example of thermodynamics, statistical mechanics, and average distributions of energy in a system.
They explain that there are macro states with classical observable properties such as temperature, volume, pressure, etc. These macro states are manifested from many micro states of particles (position, momentum, spin, etc.), and the macro state we observe correlates to the most possible (most statistically occurring) microstates.
If you arrange 180 black stones on a go board, there are 2 times 10 to the 107th power — (2)(10^107) — possible arrangements. These arrangements represent the possible micro states of particles, and by far most of these states or arrangements of stones look like a macro state of black stones evenly distributed around the board. It is a very rare micro state to have all the black stones in one corner or filling half the board. That macro state is observably quite different than the many distributions of stones around the entire board. Some micro states are so rare, like one chance in (2)(10^107) possibilities, that they never actually occur, just as we don’t suddenly experience all the oxygen in a room randomly collecting against one wall of the room.
– story edited by Bill Chiles; thanks to Freeman Ng for the story tip.
