# Is entropy of surroundings a state function?

It is a pretty common well known fact that the entropy of a system is a state function ie. it doesn't depend upon the path taken by the process as long as the initial and final states are the same.

I have a doubt whether we can say the same for surroundings or even the universe.

My first thought is that the entropy of the universe would be continuously increasing or at best it would be constant. It can never decrease. Thus the universe can never be at a state where it was before. The talk of state function seems strange here.

Still I am not very sure and I have no idea whether entropy of surroundings is a state function or not.

Any help would be appreciated. Thanks

In reality, when we talk about the surroundings, what we are referring to isn't really the entire universe, outside what we call "the system." What we are really referring to is a subregion of the entire universe, wherein it is possible to carry out changes reversibly without encompassing the whole rest of the universe. So, when we talk about the entropy change of the surroundings, we are not including spontaneous processes occurring light years away in other galaxies. And, when we say that the entropy change for system plus the surroundings is zero, we are really only including the selected subregion of surroundings chosen to represent our sub-universe.

• A proper appellation would be perhaps a light cone. Jun 18, 2020 at 22:01
• I don't feel this answers the question. Can you give a mathematical argument that the entropy of surroundings is a state function? Because I'm under the impression the entropy change of the surroundings has a different value for reversible and irreversible processes, making it path-dependent. Feb 10, 2022 at 1:01
• @electropusher Can you please give a specific example to illustrate your contention? Feb 10, 2022 at 3:30