Entropy and derivations - is my logic faulty?

[Chestermiller]

For an isolated system like the universe, the Clausius inequality reduces to $$\Delta S\gt\int{\frac{dq}{T}}=0$$This means that, even with no heat transfer to the system (dq=0), entropy is generated with the system itself, and thereby increases.

 

[PeterDonis]

The entropy of sub systems is additive

There are no "subsystems" in the Friedmann models, or in the thermodynamics based on them that you referenced. There is just one homogeneous, isotropic universe.

so the overall entropy of the universe must be greater than zero

For our actual universe, yes, I agree. For the idealized universe in the Friedmann models, however, you might want to rethink this statement.

This must be equal to T dS

No, $T dS$ is the change in entropy as a result of some process. If the process is adiabatic, as the expansion of the homogeneous, isotropic universe is in the Friedmann models, then $dS = 0$. Your references make that clear. What they do not discuss at all is what other processes might be taking place in the actual universe (as opposed to the idealized universe in the Friedmann models) that might increase entropy.

 

[Nick Prince]

No. But that does not mean I think entropy is increasing in the idealized models of a homogeneous, isotropic universe based on the Friedmann equations. Your references make it obvious that it is not. So, if entropy is in fact increasing in our universe, it is obviously doing so as a result of some process that is not included in those idealized models.

So the implicit starting assumptions are wrong and hence the friedmann's accn and continuity equation are not complete?

 

[PeterDonis]

So the implicit starting assumptions are wrong and hence the friedmann's accn and continuity equation are not complete?

Do you think the equations in the references you gave are complete models of everything that happens in the universe?

 

[Arman777]

Looks ok, I was able to get to the URL and see the quote you gave.
Yes, but this still doesn't say how energy density is related to temperature.
This T is the T of the CMB. It's not the same as the T of other components of the universe. The link you gave discusses two kinds of components: radiation (of which the CMB is an example) and cold non-relativistic matter. What is the T of the latter?

Thats nice then

Well I mean to radiation energy density. And radiation energy density has a relationship with tempature.

I mean the CMB.