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cianfa72

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- Spacetime vs thermodynamic state space as manifolds from the intrinsic vs extrinsic point of view

Hi,

I don't know if it is the right place to ask for the following: I was thinking about the difference between the notion of spacetime as 4D Lorentzian manifold and the thermodynamic state space.

To me the spacetime as manifold makes sense from an 'intrinsic' point of view (let me say all the universe lives in such manifold) whereas the thermodynamic state space as manifold actually

In other words in the thermodynamic state space case we start from an 'ambient' vector space ##\mathbb R^n## in which a physical system is

What do you think about ? Thank you.

I don't know if it is the right place to ask for the following: I was thinking about the difference between the notion of spacetime as 4D Lorentzian manifold and the thermodynamic state space.

To me the spacetime as manifold makes sense from an 'intrinsic' point of view (let me say all the universe lives in such manifold) whereas the thermodynamic state space as manifold actually

*represents*the thermodynamic state of a physical system and as manifold it makes sense only from an 'extrinsic' point of view.In other words in the thermodynamic state space case we start from an 'ambient' vector space ##\mathbb R^n## in which a physical system is

*represented*as a point in this space. Of course there exist constrains on the possible 'combination' of the state space variables/coordinates (e.g. the amount of Energy) so that the set of possible points as manifold is actually a submanifold of ##\mathbb R^n##.What do you think about ? Thank you.