In the "proof" of the theorem, my course notes defines [itex]P_r(t)[/itex] as the probability to find the system is state r at time t, and it defined H as(adsbygoogle = window.adsbygoogle || []).push({}); the mean valueof [itex]\ln P_r[/itex] over all acesible states:

[tex]H \equiv \sum_r P_r\ln P_r[/tex]

Is is right to call the above sum the "mean value of ln P_r" ?! Cause given a quantity u, the mean value of f(u) is defined as

[tex]\sum_i P(u_i)f(u_i)[/tex]

So the mean value of [itex]\ln P_r[/itex] should be

[tex]\sum_r P(P_r)\ln P_r[/tex]

But P(P_r) does not make sense.

I confessed my confusion to the professor in more vague terms (at the time, I only tought the equation looked suspicious), but he said there was nothing wrong with it. I say, H could be called at best "some kind" of mean value of ln(Pr).

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# Mathematical detail regarding Boltzman's H thm

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