Can the universe be considered a thermodynamic system? With matter a type of energy, can/should the universe be considered a thermodynamic system? At what scale would it be relevant?
 A: Although it is attempting to apply thermodynamics to the whole universe, and some of the founding fathers of Thermodynamics did it, a closer inspection of the problem would suggest some caution.
Let me list the major difficulties one faces when trying to apply thermodynamics to the entire universe.
The system

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*Do we know or control what is our system? The observable universe is not the whole universe. Is it possible to say something on a system we do not fully control? And what about the interaction with the non-observable universe?


*Even if we consider the whole universe (observable and not-observable) as our system, we do not know very much about it. In particular, there is no proof that the energy of the whole universe is constant.
What a thermodynamic system is?

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*A thermodynamic system is a system of many degrees of freedom which can be described by a bunch of variables, due to the simplifying property of thermodynamic equilibrium. Certainly, this is not the case of our present universe.

*A less demanding requirement, still allowing for a thermodynamic description, would be the hypothesis of Local Thermodynamic Equilibrium (LTE). However, we know for sure that LTE is a good approximation in many cases, but not always.

Non-standard thermodynamics

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*Even if we limit our attention to subsets of the universe large enough that gravitational interaction plays the most important role, the properties of such systems are not standard. It is well known that gravitational systems have non-extensive thermodynamics and negative specific heat.

In a way, this last observation enables us to approximately identify the scale where gravitational interactions start to dominate as the limiting scale for usual thermodynamics.
My final conclusion is that the application of thermodynamics to the whole universe requires much more care than usually thought. Concepts like the energy or the entropy of the universe cannot simply be extrapolated from the usual meaning in a laboratory. Without an explicit theory, they are just meaningless words.
A: In thermodynamics theoretically anything can be defined as a system. But in so doing one must also consider what would constitute the system's surroundings and the boundary between the system and its surroundings. In that regard, if the universe were defined as a thermodynamic system, then what would constitute its surroundings? Its boundary? (especially if the universe is expanding). And with what would the system exchange mass and/or energy (work and/or heat) with?
So you see, it appears your question only raises more questions than answers. But I'm  not a cosmologist. Perhaps a cosmologist can provide a better answer.
In any event, hope this helps.
A: It is the nature of understanding the cosmology of the observable universe that we assume as an axiom, regarding a cosmological model, that at a large scale it is homogeneous. It is impossible to know what is actually going on in that part of the universe which is not part of our observable universe. However, this fact has no relevance to whether or not a model can exist which includes the characteristic of being a thermodynamic system. However, I do remember reading somewhere (no memory of where and possibly erroneous) that there are constraints from general relativity (GR) that might possibly prevent a consistent model from combining both GR and thermodynamics.
