Zeh's definition of entropy production and the second law

[nonequilibrium]

Hello, I was reading Zeh's "The Physical Basis of the Direction of Time" but I just can't understand him in chapter 1 on something really easy: the definition of the phenomenological entropy + second law. Here is a screenshot I took from the googlebooks edition:

Those two lines of formulas really confuse me, for several reasons. The most obvious one:

He says $$\left( \frac{dS}{dt} \right)_{int} \geq 0$$

But I thought the 2nd law clearly stated $$\frac{dS}{dt} \right \geq 0$$
After all: a system in connection to a reservoir doesn't have to go up in entropy.

Can anybody clear this up for me?

 

[Mapes]

Agreed; Zeh should have $\frac{dS}{dt}\geq 0$. As written, his equation would prohibit a hot object from cooling to room temperature, since internal entropy would decrease in that scenario.

 

[Andy Resnick]

Zeh defined the heat flux as passing inward to the system, which would require the internal entropy increase or remain constant.

Something else appears sloppy- 'S' refers to a bounded system, which is then composed of internal S_int and external S_ext components?

 

[Mapes]

Zeh defined the heat flux as passing inward to the system, which would require the internal entropy increase or remain constant.

That's a good point, but wouldn't one just take that as a sign convention - that positive $dQ$ implies inward heat transfer - rather than a restriction that $dQ$ remain positive? It doesn't make much sense to define your thermodynamics framework based on systems that can only gain heat.

 

[Andy Resnick]

Agreed, there's a lot in the blurb that does not make sense. Maybe it's covered elsewhere in the book...

 

[nonequilibrium]

Hm, not really covered elsewhere no (it's from the beginning of chapter 3, which I've read now, and it's the only one talking about classical thermodynamics). Oh well, I'm happy that at least I'm not the only one confused. Another thing that is weird, is that if dQ is positive if heat is going in the "interior", then I'd say dS_ext = -dQ/T (although not even that could be correct, because the "exterior" is not infinite due to the quote from Resnick about the total system being bounded...). Very weird situation.