Maria and Hernando Quevedo proposed a geometric interpretation of this field of physics in terms of a contact structure invariant under Legendre transformations. For 10 points each:
[10m] Name this field of physics. Since this field often analyzes functions with an exact differential form, Constantin Carathéodory was able to develop an axiomatization of it using Pfaffian differential equations.
ANSWER: thermodynamics [accept geometrothermodynamics or geometrical thermodynamics]
[10e] The most notable contribution of Carathéodory’s axiomatization of thermodynamics is his expression of this law that concerns the increase of entropy in closed systems.
ANSWER: second law of thermodynamics
[10h] Carathéodory introduced this relation in his axiomatization of the second law, and his namesake principle guarantees that there exist states in the neighborhood of any state X that do not have this relation to X. Lieb and Yngvason elaborated on the view of this concept as an ordering relation that defines entropy.
ANSWER: adiabatic accessibility [accept adiathermal accessibility]
<SM, Physics>