Relationship between thermodynamics and differential geometry

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SUMMARY

The discussion centers on the intersection of thermodynamics and differential geometry, particularly the application of state spaces isomorphic to R3 in the context of thermodynamic equations. The participant explores defining surfaces based on the equation PV=NkT and considers quasi-static state equations as curves on these surfaces. They seek resources that address undergraduate-level thermodynamics from a differential geometry perspective, noting that existing literature tends to focus on more advanced topics. The concept of thermodynamic phase space as a 'contact manifold' is highlighted, contrasting it with the symplectic manifold of classical mechanics.

PREREQUISITES
  • Understanding of thermodynamic principles and equations, specifically PV=NkT.
  • Familiarity with differential geometry concepts, particularly state spaces and manifolds.
  • Knowledge of the differences between contact and symplectic manifolds.
  • Basic research skills to locate academic papers and texts on specialized topics.
NEXT STEPS
  • Research "thermodynamic phase space as a contact manifold" for foundational understanding.
  • Explore undergraduate-level texts on thermodynamics that incorporate differential geometry.
  • Investigate the application of quasi-static processes in thermodynamics.
  • Study the differences between contact and symplectic manifolds in the context of physics.
USEFUL FOR

Students of thermodynamics and differential geometry, educators seeking interdisciplinary resources, and researchers interested in the mathematical foundations of thermodynamic principles.

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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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