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I think statistical and residual are the same except that for residual entropy, the system does not account for thermal entropy, meaning T=0. I think the large error in W means that there is a large error in determining the number of states possible? This part I am not too sure.
I think that the statements above are correct, as a large error in W (degeneracy) constitutes a small error in the residual entropy. It seems that the residual entropy is flexible to the errors in W. But, as always it doesn't count the thermal entropy we can calculate using the same equation.
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