- #1
raeed
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I was reading the derivation of Boltzmann distribution using the reservoir model.
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 = gA ⋅ gR
- if gR goes up then gA has to go down meaning gA ∝ gR
- P(e) ∝ 1/gA → P(e) ∝ gR
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
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 = gA ⋅ gR
- if gR goes up then gA has to go down meaning gA ∝ gR
- P(e) ∝ 1/gA → P(e) ∝ gR
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