Relationship between thermodynamics and differential geometry

AI Thread Summary
The discussion highlights the overlap between thermodynamics and differential geometry, particularly through the concept of state spaces and surfaces defined by equations like PV=NkT. The participant is exploring whether this geometric approach to thermodynamics is beneficial and if it has been studied at a basic undergraduate level. They note that existing literature often delves into more advanced topics, leaving a gap for foundational studies. The relationship between thermodynamic phase space and contact manifolds versus symplectic manifolds in classical mechanics is also emphasized. Overall, the inquiry seeks resources that bridge these two fields at an introductory level.
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I am taking thermodynamics this semester as well as a course in differential geometry of surfaces, and I am seeing a lot of overlap.

For example, I can create a "state space" isomorphic to R3 of TxPxV I can then define a surface on this space of PV=NkT I can define quasi static state equations as curves restricted to the surface.

Is this an approach a useful approach to thermodynamics? Is this studied at all? I Googled "Thermodynamics differential geometry" and got results that were about much more advanced topics in thermodynamics. Is there a text, or paper, studying basic (I am taking an undergrad course) thermodynamics from this perspective?
 
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