TITLE: Are there any books/articles that apply abstract coordinate free differential geometry to basic thermodynamics?
QUESTION [10 upvotes]: The mathematical structure of thermodynamics by Peter Salamon (pdf) would be an example, but i would like a more abstract natural formulation of application of differential geometry or even geometric algebra to for example Maxwell relations in thermodynamics that does not use coordinates.

REPLY [3 votes]: In this context, one should probably mention "Contact Geometry: the Geometrical Method of Gibbs's Thermodynamics" by V.I. Arnold (Proc. of the Gibbs Symposium,Yale University, 1989, 163-179).