I aim at developing a geometrical formulation of thermodynamics by employing contact geometry and associated notions. A geometric formulation of thermodynamics is of interest for several reasons. Firstly, geometry serves as a language in which every physical theory can be formulated, it provides geometric tools and notions which can be employed to infer new principles and ideas, and in general promotes mathematical beauty in physics. Secondly, a geometrisation of thermodynamical theories would help to systemize and unify the phenomenologically orientated formulations and derivations of thermodynamical phenomena and potentially be of great use in the description of non-equilibrium scenarios. And finally, due to the fundamental connection of the laws of black hole thermodynamics with their geometry, there is the hope that a geometric theory of thermodynamics could lead to new insights into black hole thermodynamics and the physical laws governing the physics of black holes.
After an introduction into the mathematics of the subject, I will introduce possible applications of contact geometry and its formulation of thermodynamics in non-equilibrium systems and black holes, respectively.
