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  • $\begingroup$ So you're saying it should be $0$ as presented? $\endgroup$
    – BioPhysicist
    Commented Apr 17 at 17:53
  • $\begingroup$ @BioPhysicist Yes. Since $dU_{R}=\delta Q_{R} $ we have $dS_{R}=- \delta Q_{R}/T_{R}$ and $dS_{sys}=+\delta Q_{R}/T_{R}$ making $dS_{total}=0$. $\endgroup$
    – Bob D
    Commented Apr 17 at 18:10
  • $\begingroup$ But then he talks about a change in the total entropy of the universe. So there must be some disconnect between the derivation and the conclusion. I'm confused on which part breaks down. $\endgroup$
    – BioPhysicist
    Commented Apr 18 at 1:48
  • $\begingroup$ @BioPhysicist. I think (but I’m not sure) I may have found the disconnect. To me the only possible conclusion is dF must be zero. But not being conversant with Helmholtz free energy I looked at the Wikipedia article in which they also acknowledge it would seem dF would have to be zero but there is no contradiction. It appears it has something to do with expanding the number of particles in the system in the system, which I discounted since dN of the reservoir is zero. $\endgroup$
    – Bob D
    Commented Apr 18 at 9:27
  • $\begingroup$ Not being good at chemistry I don’t quite understand why. The relevant section in the article is Minimum Free Energy and Maximum Work Principles $\endgroup$
    – Bob D
    Commented Apr 18 at 9:27