| Abstrakt: |
Thermodynamics is easier to understand if it is put in a geometric context. Arnold (1990) has stated, ˵Every mathematician knows that it is impossible to understand any elementary course in thermodynamics. The reason is that the thermodynamics is based – as Gibbs has explicitly proclaimed – on a rather complicted mathematical theory, on the contact geometry″. This comment refers to thermostatics, but an extended contact structure applies to non-equlibrium thermodynamics as well. Homogeneous thermodynamics is geometrically represented in a contact manifold by a codimension one submanifold which is locally the graph of the generalized energy function, ᵠ*. The graph of the generalized function contains the thermostatic system as a Legendre submanifold. Equilibrium or non-equilibrium processes are paths on the corresponding portions of the graph. The relationship of the graph of the thermodynamic energy function and the graph of the thermostatic energy function is defined by a cross-section of a vector bundle. An alternative definition of the thermostatic manifold is obtained as a Lagrange submanifold defined by the symplectic two-form associated to the Gibbs contact one-form. [ABSTRACT FROM AUTHOR] |
