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lets call the reservoir by index R and the tiny system by index A.

In the derivation they proposed that the probability for being at energy e (for A) is proportional to the number of states in reservoir. I didn't understand this completely and i would be happy to get some help!

here is my take on it, and please correct me if I'm wrong.

- The temperature of the whole system is T and it's constant therefor the number of states for the whole systems g is also constant

- both A and R are independent of each other therefor g = g

_{A}⋅ g

_{R}

- if g

_{R }goes up then g

_{A}has to go down meaning g

_{A}∝ g

_{R}

- P(e) ∝ 1/g

_{A}→ P(e) ∝ g

_{R}

I'm not really convinced by my explanation so if someone could explain it and perhaps give me an intuitive physical explanation, I'd be happy. Thank you