J. Non-Equilib. Thermodyn. Vol. 18 (1993), pages 51-57 On the Global Symmetry off Thermodynamics and Onsager's Reciprocity Relations K. Gambar, R Markus Institute of Physics, Technical University of Budapest, Budapest, Hungary Communicated by J. Verhas Registration number 572 Abstract We apply the Hamiltonian variational principle to the thermodynamic equation of motion in convection- and source-free systems. We show that the Onsager Reciprocity Relations are consequences of the global gauge symmetries of the Lagrangian which is related to the entropy production of the processes considered. Introduction Onsager's reciprocity relations [1—5] are very important in non-equilibrium thermodynamics because they reduce the number of independent coefficients. Their general validity follows from the hypothesis of microscopic reversibility, with the latter being verified by fluctuation theroy. Fluctuation theory, however, is based on a hypothesis of mechanical origin alien both to phenomenological thermodynamics and thermodynamic field theory. Some scientists accept Onsager's reciprocity relations in non-equilibrium thermodynamics (regardless of whether they accept his proof or not), others do not accept them and do not use them at all [1-23]. The reciprocity relations can be proved within the framework of the field theory of thermodynamics in several ways. We show that Onsager's reciprocity relations are the consequences of the existence of the Hamiltonian variational principle in the field theory of non-equilibrium thermodynamics. The Hamiltonian variational principle of thermodynamics The linear transport equations for convection- and source-free systems are (i) J. Non-Equilib. Thermodyn., Vol. 18, 1993, No. 1 © Copyright 1993 Walter de Gruyter · Berlin · NewYork Brought to you by | Purdue University Libraries Authenticated Download Date | 5/29/15 3:29 AM