Open and closed in the geometrical sense vs the thermodynamic sense

[WraithM]

"Open" and "closed" in the geometrical sense vs the thermodynamic sense

Perhaps this is a silly question, but what is the relationship between the words "open" and "closed" in the geometrical sense (open, flat, closed universes) and in the thermodynamic sense (open and closed systems) in the context of General Relativity? Is there no connection at all? Is there such a thing as a closed thermodynamic system and an open geometry or visa versa? Must a closed geometry be a closed thermodynamic system and visa versa?

I have a basic understanding of GR, and I understand a lot of the math behind it, so don't be afraid to give me a technical explanation.

Thank you!

 

[zhermes]

They're different ideas. Open and closed with regards to thermodynamics is just referring to whether heat can be lost (open) or if energy is internally conserved (closed).

In GR, open and closed refer to geometries of 4d space-time, depending on if the density (omega) is greater or less than 1. If the universe is closed, it will contract again (the big crunch), if its open it will continue to expand indefinitely. There are some other effects (e.g. the sum of angles in a triangle), but I think you get the idea.

 

[WraithM]

They're different ideas. Open and closed with regards to thermodynamics is just referring to whether heat can be lost (open) or if energy is internally conserved (closed).

In GR, open and closed refer to geometries of 4d space-time, depending on if the density (omega) is greater or less than 1. If the universe is closed, it will contract again (the big crunch), if its open it will continue to expand indefinitely. There are some other effects (e.g. the sum of angles in a triangle), but I think you get the idea.

I know the definitions of both. I was looking for the connection between the two. I fully understand that they're different ideas. Perhaps I didn't make myself clear in the question, but I meant how is the geometry related to thermodynamics? As I said, is it possible for a closed geometry to be an open system and visa versa? Or must an open geometry be an open system?

I've taken a course on basic GR and thermodynamics. I've just never dealt with the cosmological aspects of GR.

 

[zhermes]

I know the definitions of both. I was looking for the connection between the two. I fully understand that they're different ideas.

Not so sure about that. See: http://en.wikipedia.org/wiki/Homonym"

 

[WraithM]

Not so sure about that. See: http://en.wikipedia.org/wiki/Homonym"

Calm down.

 

[zhermes]

Sorry, unfortunately some of the people around these forums are rubbing off on me...
What I MEANT TO SAY was, the two ideas are quite separate. I guess, one would say that both open and closed geometries are closed thermodynamic systems because they are entire 'universes' (independent entities) of sorts, but I think that's straying from what you're asking.

CORRECTION: open and closed geometries can also refer to regions of curvature (I think), in which case there is really no relation between them and thermodynamics per se.

 

[WraithM]

Sorry, unfortunately some of the people around these forums are rubbing off on me...
What I MEANT TO SAY was, the two ideas are quite separate. I guess, one would say that both open and closed geometries are closed thermodynamic systems because they are entire 'universes' (independent entities) of sorts, but I think that's straying from what you're asking.

CORRECTION: open and closed geometries can also refer to regions of curvature (I think), in which case there is really no relation between them and thermodynamics per se.

Thanks, that actually completely answers my question. Forums turn people into internet tough guys. It's all good :)