A while ago in December I did a quick simulation of ideal gas particles in a cube and how their speeds change over time. The mathematics is really quite interesting and over time the velocities approach the Maxwell-Boltzmann distribution. It’s an interesting derivation and there is quite a beautiful derivation from Maxwell based on symmetry arguments alone. I wrote up my version of this argument and it is included on this page.

The MATLAB code for the simulation I did (and a dump of all sorts of data files that I haven’t quite sorted out since) is at my GitHub repository as well as my writeups, but for quick access I’ve included the code writeup below too.

### Simulation writeup

Direct link to PDF

Ideal Gas Simulation

### Mathematical derivation

Direct link to PDF

Boltzmann Distribution Derivation