On the intrinsic geometric structure of extended irreversible thermodynamics

In this paper we reexamine the geometric structure of extended irreversible thermodynamics in the context of contact geometry. First, we consider the interplay between the contact manifold (M, ω) with thermodynamic state space BN as its base, and the cotangent bundle T*BN equipped with a nondegenerate 2-form Ω = dω. We then show that the Legendre submanifold L of M and the Lagrangian submanifold of T*BN are intimately related to the entropy surface of the thermodynamic system. Second, we further generalize the symmetry transformations considered in our previous work that preserve the laws of thermodynamics as well as the pseudo-Riemannian metric in L. Finally, we consider some examples on coordinate transformations in M that illustrate the transformation between the entropy surface and the energy surface, and the relationship between Legendre involution and the submanifold of (T*BN, Ω)