What do we meant by "Thermally isolated universe"? As we knew in general,
$$dS=\frac{\delta Q_{rev}}{T}\geq \frac{\delta Q}{T}.$$
Consider a thermally isolated system so that the above inequality becomes
$$dS\geq 0 \ \ \text{if} \ \ \ \delta Q=0. $$
And so we say that the second law of thermodynamics can be written as : Assuming that the universe can be treated as an isolated system,
$$S_\text{universe} \ \text{can only increase}.$$

The question is what we really meant by the isolated universe?
If you look for the definition of the system it says, a system to be whatever part of the universe we select for study, and near the system are its surrounding. Now this definition contains the universe already. What did we mean by the surrounding of the universe to which it is isolated? Also, what's the boundary of this universe system?
 A: When we say "universe," what we really mean is the system plus its local surroundings.  The local surroundings are such that they can only exchange work and heat with the system, and not with anything else.
A: I agree with @Chet Miller answer with respect to what is practically referred to in thermodynamics as the "universe": i.e., it is the combination of the system plus its local surroundings.
In theory, the system can be anything you wish to define it to be. That would theoretically include the possibility of defining the universe as the system. But when you do define the system, that definition needs to include the following things that may be considered, at best, problematic, if one wishes to define the system as the universe:

*

*The properties (contents) of the system.


*Everything not included in (1) constitutes the surroundings.


*The system boundaries. The system boundaries can be real (physical) or imaginary, fixed or moveable, open or closed. It is the character of the system boundaries that determines the possibility of mass and/or energy exchange between the system and its surroundings. In other words, the boundary determines whether or not the system is isolated (unable to exchange mass or any form of energy with its surroundings).
I submit that, with respect to the universe, we do not know the complete answer to (1) (see link below). If the universe is everything then there are no surroundings (answer to 2) If there are no surroundings, then there is no boundary (answer to 3). So given all of this, what then is the universe "isolated" from?
https://blogs.scientificamerican.com/life-unbounded/this-is-what-we-done28099t-know-about-the-universe/
Hope this helps.
