My talk will make the following points:
- Go from probabilities to the entropy via so-called uniqueness theorems. We shall meet 4 such entropies: S-R, S-S, S-T, S-U, only
one of which (Shannon's S-S) is in common use.
- By maximisation we find relations for probabilities, entropies, etc. so that we can find equilibrium statistical mechanics.
- We note that some extensions for non-equilibrium situations are possible.
- Thermodynamics leads to the suggestion: arithmetic mean > geometric mean.
- One can decouple disorder and entropy.
- Using the black hole entropy, the universe looks orderly.