Comments on the existence of Hamiltonian principles for non-selfadjoint operators

Abstract

The thermodynamic transport equations contain the first time derivative, a non self-adjoint operator, which makes it impossible to derive them from Hamilton's variational principle. However, introducing new basic fields which generate measurable properties in the same way as the potentials in other held theories, the complete Hamilton Lagrange formalism may be established. This fact ostensibly surpasses Finlayson's work where special restrictions for classical variational principles are given. We point out that although these restrictions seem to preclude the construction of a variational scheme for the transport equations, a correct interpretation of these facts permits to solve this apparent paradox. The Onsager reciprocal relations play a central role in the compatibility between these two apparent opposite views.