Symplectic structure of equilibrium thermodynamics.

The contact geometric structure of the thermodynamic phase space is used to introduce a novel symplectic structure on the tangent bundle of the equilibrium space. Moreover, it turns out that the equilibrium space can be interpreted as a Lagrange submanifold of the corresponding tangent bundle, if the fundamental equation is known explicitly. As a consequence, the Hamiltonian description of thermodynamics is obtained in a natural way and a Hamilton-Jacobi-like equation is introduced whose solutions determine entire families of thermodynamic systems.