Thermodynamics from the differential geometry standpoint

We study the differential-geometric structure of the space of thermodynamic states in equilibrium thermodynamics. We demonstrate that this space is a foliation of codimension two and find variables in which the foliation fibers are flat. We show that we can introduce a symplectic structure on this space: the external derivative of the $1$-form of the heat source, which has the form of the skew-symmetric product $dT\wedge dS$ in the found variables. The entropy $S$ then plays the role of the Lagrange function (or Hamiltonian) in mechanics, completely determining the thermodynamic system.