Clarification on an explanation during the lecture

[Ernie Lee 3F]

Hello, when Professor Lavelle mentioned Thermodynamical property ("Small" error in S) and Statistical property ("Large" error in W), was it to explain that even with a large W value, there won't be a significant change in S?

[Gregory_Kislik_2C]

Yes. Because of the ln in the equation deltaS = kblnW, large changes in W will result in small changes in S, so the relative uncertainty is small in S despite it being large in W.

For example, take a sample of five particles of BF2Cl, which has three possible positions. The resulting number of microstates is 3^5, or 243 = W.

Entropy however, turns that 3^5 into a 5ln3 (multiplied by the Boltzmann constant), which makes it a much smaller number.

I hope this helps, please let me know if there are any errors.