Hard Sphere Chemical Potential
Chemical potential is an entropy difference
For hard spheres, the energy is zero or infinity
- any change in N that does not cause overlap will be change at constant U
To get entropy difference
- simulate a system of N+1 spheres, one non-interacting “ghost”
- occasionally see if the ghost sphere overlaps another
- record the fraction of the time it does not overlap
Here is an applet demonstrating this calculation