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.