Boltzmann in JavaLand

I found this rather impressive java applet that simulates a box of bouncing balls. This java applet makes it easy to picture how the Second Law of Thermodynamics works.

The Second Law of Thermodynamics was the master-work of the great 19th centur physicist, Ludwig Boltzmann. Boltzmann gazed into the heart of the Second Law of Thermodynamics and found statistics. Then he rephrased the Second Law of Thermodynamics in terms of statistics: the probability of the system increases until it reaches the maximum probability.

What does that mean for our box of balls? Since thermodynamics deal with energies, it turns out that the speed of a ball is a great proxy for its' energy. So for a slice of time, you can count how often any of the balls has a certain speed. And so the probability of a box of balls can be understood as the distribution of speeds of the balls. This distribution is the probability that Boltzmann is getting at.

So the Second Law of Thermodynamics for a box of balls means that (1) there is an ultimate distribution of speeds, which we call the "equilibrium distribution" (the formula for this was derived by James Clerk Maxwell), and (2) any collection of balls will collide and mix-up their speeds until the distribution of speeds reaches this equilibrium distribution, after which no matter how the balls collide further, the distribution will not really change any more.

In this java applet, you can see how distribution of speeds change over time, as the balls do their thing and collide. Be sure you play around with the "parameters" - reduce the number of balls and bump up the radius of the balls. See how the Second Law works as the distribution of speeds changes inexorably towards the equilibrium distribution, even for a few balls.