Relativistic Theory of Irreversible Thermodynamics for Multi-Component Fluids and Its Post-Newtonian Limit in Relation to Classical Extended Thermodynamics

Abstract

AbstractFirst, the special-relativistic Theory of Irreversible Processes for a multi-component fluid is formulated. It is based on (i) the balance equations of the particle number and the energy-momentum for the total system (i. e., the mixture of the components) as well as the sub-systems (i. e., the components) and (ii) the dissipation inequality and the Gibbs equation for the mixture. In order to allow for reactions between the single components, in contrast to the total system, the sub-systems are assumed to be open, which means that their particle number and energy-momentum are not constrained by conservation laws. Without making any assumptions on the thermodynamic behavior of the interacting components, one arrives at a thermodynamic description of the mixture showing now heat conduction and viscosity. In particular, this makes it possible to calculate the entropy production and, thus, to identify thermodynamic currents and forces. In a second part, the post-Newtonian limit of this theory is calculated to show that for the mixture there result relations known from classical Extended Thermodynamics that partly are corrected by entrainment terms. The mathematical origin and physical consequences of these terms are discussed.