Ensemble Volumes
Entropy and free energy relate to the size of the ensemble
No effective way to measure the size of the ensemble
- no phase-space function that gives size of R while sampling only R
imagine being place repeatedly at random points on an island
what could you measure at each point to determine the size of the island?
Volume of ensemble is numerically unwieldy
- e.g. for 100 hard spheres
r = 0.1, W = 5 ? 10133
r = 0.5, W = 3 ? 107
r = 0.9, W = 5 ? 10-142
Shape of important region is very complex
- cannot apply methods that exploit some simple geometric picture
W = number of states of given E,V,N