The aim of this paper is to develop the field theory of nonequilibrium thermodynamics by the Hamiltonian formalism and to prepare an alternative foundation for the theory. We give the Lagrangian from which the field equations as Euler-Lagrange differential equations can be derived. We point to the canonically conjugated quantities and then we give the Hamiltonian. We deduce the canonical field equations and we explain the Poisson-bracket expressions. From the Poisson-bracket expression of the entropy density and the Hamiltonian we find that the entropy density is a bilinear expression of the current densitites and the thermodynamic forces. At the end of this paper we deal with the invariance properties of irreversible thermodynamics. We show that geometrical transformations do not lead to new conserved quantities. Finally we give a dynamical transformation by which the Lagrangian is invariant and we see that the reciprocity relations are the consequences of this inner symmetry. We think that this Hamilton-Lagrange formalism of thermodynamics may be interesting and important not only for thermodynamics.

• Received 10 December 1993

DOI:https://doi.org/10.1103/PhysRevE.50.1227