Geometry of phenomenological thermodynamics

This paper attempts to justify the proposal that the accurate geometrical description of the phenomenological thermodynamics of equilibrium (PTE) should be based on the assumption that the phase space of PTE is an even-dimensional manifold, that the internal energy, no longer a basic coordinate, forms, together with other thermodynamic potentials, an algebraic lattice, and that PTE is therefore a superposition of symplectic structure of the phase space and of lattice structure of thermodynamic potentials. It concludes that the geometrization of PTE in terms of even-dimensional symplecticspace seems to be more profound than the usually suggested odd-dimensional contact manifold approach. The proposal is supported by the fact that thermodynamic potentials can now be defined in a rigorous geometrical way in which they reveal the structure of a lattice. 11 references, 2 figures