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Takeaways:

Never trust quantities stated as ground truth. Like for example any mention of energy is assumed to be averaged lol.

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Always about how significant energy overcomes randomness.

Feynman quote: “We will now start to take some of these steps, but while many of our analyses will be quite accurate, they will eventually get less and less accurate. We will have only a rough understanding of the properties of matter.”

1. Microstate definition

A microstate is a complete assignment of every particle to a specific energy level.

• You have 3 distinguishable particles (say labeled 1, 2, 3).
• You have 2 levels (call them E1,E2E_1, E_2E1,E2).
• A microstate looks like:
  • (1 at E1E_1E1, 2 at E1E_1E1, 3 at E2E_2E2)
  • or (1 at E2E_2E2, 2 at E1E_1E1, 3 at E1E_1E1), etc.

Each particle’s placement matters → order matters.

2. Macrostate (configuration number)

A macrostate is specified only by how many particles occupy each level, not which ones.

• Example: “2 in E1E_1E1, 1 in E2E_2E2” is a macrostate.
• Example: “3 in E1E_1E1, 0 in E2E_2E2” is another macrostate.

So a macrostate = a set of occupation numbers

(n1,n2)with n1+n2=N.(n_1, n_2) \quad \text{with } n_1+n_2 = N.

(n1,n2)with n1+n2=N.

Here: possible macrostates = (3,0), (2,1), (1,2), (0,3).