Two Approaches to the Description of the Evolution of Thermodynamic Systems*

This paper analyses two approaches to the description of thermodynamic evolution. The first approach describes the dynamics of a thermodynamic system by contact vector fields extended with inputs and outputs while the second one interprets the thermodynamic vector field as a smooth section of the tangent bundle of the respective Legendre manifold parametrized by n functions, called thermodynamic controls. It is shown that there is a duality between these two approaches similar to the one found in the symplectic case. However, there are still many open questions which present a waste opportunity for further research.