The mathematical structure of thermodynamics Peter Salamon https://www.google.hr/url?sa=t&source=web&rct=j&url=http://www.sci.sdsu.edu/~salamon/MathThermoStates.pdf&ved=2ahUKEwjNmZm76rfaAhUMhqYKHYEhB3EQFjABegQIAxAB&usg=AOvVaw2oVkivqEpruSfubsaFluRX

This 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.

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.