HAMILTON-LAGRANGE FORMALISM OF NONEQUILIBRIUM THERMODYNAMICS

The aim of this paper is to develop the field theory of nonequilibrium thermodynamics by the Hamiltonian formalism and to prepare an alterna tive foundation for the theory. We give the Lagrangian from which the field equations as Euler-Lagrange differential equations can be derive d. We point to the canonically conjugated quantities and then we give the Hamiltonian. We deduce the canonical field equations and we explai n the Poisson-bracket expressions. From the Poisson-bracket expression of the entropy density and the Hamiltonian we find that the entropy d ensity is a bilinear expression of the current densities and the therm odynamic forces. At the end of this paper we deal with the invariance properties of irreversible thermodynamics. We show that geometrical tr ansformations do not lead to new conserved quantities. Finally we give a dynamical transformation by which the Lagrangian is invariant and w e see that the reciprocity relations are the consequences of this inne r symmetry. We think that this Hamilton-Lagrange formalism of thermody namics may be interesting and important not only for thermodynamics.