Relativistic thermodynamics of irreversible processes I. Heat conduction, diffusion, viscous flow and chemical reactions; formal part

Abstract

The relativistic thermodynamics of irreversible processes is developed for an isotropic mixture in which heat conduction, diffusion, viscous flow, chemical reactions and their cross-phenomena may occur. The four-vectors, representing the relative flows of matter, are defined in such a way that, in the four-dimensional space-time continuum, they are perpendicular to the four-vector which represents the barycentric velocity. The entropy balance is derived from the fundamental relativistic macroscopic laws. If n is the number of chemical components, we find n + 4 relations among the 4n + 4 phenomenological equations which we obtain for the relative flows of matter and the heat flow. Owing to these relations we retain just that number (3n) of independent equations which would be expected from physical considerations. It is shown that the Onsager relations are Lorentz invariant. A new cross-effect is found between diffusion and heat conduction, arising from a relativistic term in the force conjugate to the heat flow. It appears that due to this cross-effect the diffusion phenomena are influenced by the barycentric motion.