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I do not quite understand how Brillouin goes from [tex]k\cdot \Delta (\log P)[/tex] to [tex]-k\cdot \frac{p}{P_0}[/tex] in this context:
Could anybody offer a meaningful explanation?
[I added the "The entropy decrease is then"-bit because the tex wouldn't display properly.]
from "Maxwell's Demon cannot operate: Information and Entropy", L. Brillouin, 1950.Once the information is obtained, it can be used to decrease the entropy of the system. The entropy of the system is
[tex]S_0=k\ln P_0[/tex]
according to Boltzmann's formula, where [tex]P_0[/tex] represents the total number of microscopic configurations (Planck's "complexions") of the system. After the information has been obtained, the system is more completely specified. P is decreased by an amount p and P_1=P_0-p . The entropy decrease is then
[tex]\Delta S_i = S-S_0 = k\cdot \Delta (\log P) = -k\cdot \frac{p}{P_0}[/tex]
It is obvious that p<<P_0 in all practical cases.
Could anybody offer a meaningful explanation?
[I added the "The entropy decrease is then"-bit because the tex wouldn't display properly.]
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