EXAMINATION OF PHENOMENOLOGICAL COEFFICIENT MATRICES WITHIN THE CANONICAL MODEL OF FIELD-THEORY OF THERMODYNAMICS

The field equations of linear irreversible thermodynamics have been de duced from Hamilton's principle. The Hamiltonian formalism has been co nsidered as a theory of conservative systems without dissipative proce sses. In this paper, we present the field equations of linear irrevers ible thermodynamics that are deduced from a Hamiltonian principle. Fir st, we present the canonical mathematical model for purely dissipative transport processes. Then introducing a Lie algebra of the potentials with the help of an algebraic-type transformation, we examine the phy sical processes in this algebra. We expect that two kinds of descripti ons of the same physical situation develop into two such descriptions in time, which describe the same physical situations as well. Since th e given transformation is a dynamical transformation (it leaves the La grangian invariant) in the sense of the above-mentioned expectation, w e expect that the entropy density function and the entropy production density function (which pertains to the same physical situation) have to be invariant under that transformation which leaves the Lagrangian invariant. It is shown that these are satisfied if the phenomenologica l coefficient matrices are symmetric.