Examination of phenomenological coefficient matrices within the canonical model of field theory of thermodynamics

Abstract

The field equations of linear irreversible thermodynamics have been deduced from Hamilton's principle. The Hamiltonian formalism has been considered as a theory of conservative systems without dissipative processes. In this paper, we present the field equations of linear irreversible thermodynamics that are deduced from a Hamiltonian principle. First, 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 physical processes in this algebra. We expect that two kinds of descriptions of the same physical situation develop into two such descriptions in time, which describe the same physical situations as well. Since the given transformation is a dynamical transformation (it leaves the Lagrangian invariant) in the sense of the above-mentioned expectation, we 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 phenomenological coefficient matrices are symmetric.