Entropy Identity and Material-Independent Equilibrium Conditions in Relativistic Thermodynamics

On the basis of the balance equations for energy-momentum, spin, particle and entropy density, an approach is considered which represents a comparatively general framework for special- and general-relativistic continuum thermodynamics. In the first part of the paper, a general entropy density 4-vector, containing particle, energy-momentum, and spin density contributions, is introduced which makes it possible, firstly, to judge special assumptions for the entropy density 4-vector made by other authors with respect to their generality and validity and, secondly, to determine entropy supply and entropy production. Using this entropy density 4-vector, in the second part, material-independent equilibrium conditions are discussed. While in literature, at least if one works in the theory of irreversible thermodynamics assuming a Riemann space-time structure, generally thermodynamic equilibrium is determined by introducing a variety of conditions by hand, the present approach proceeds as follows: For a comparatively wide class of space-time geometries the necessary equilibrium conditions of vanishing entropy supply and entropy production are exploited and, afterwards, supplementary conditions are assumed which are motivated by the requirement that thermodynamic equilibrium quantities have to be determined uniquely.Comment: Research Paper, 30 page

Spin Axioms in Relativistic Continuum Physics

The 24 components of the relativistic spin tensor consist of 3+3 basic spin fields and 9+9 constitutive fields. Empirically only 3 basic spin fields and 9 constitutive fields are known. This empirem can be expressed by two spin axioms, one of them identifying 3 spin fields, and the other one 9 constitutive fields to each other. This identification by the spin axioms is material-independent and does not mix basic spin fields with constitutive properties. The approaches to the Weyssenhoff fluid and the Dirac-electron fluid found in literature are discussed with regard to these spin axioms. The conjecture is formulated, that another reduction from 6 to 3 basic spin fields which does not obey the spin axioms introduces special material properties by not allowed mixing of constitutive and basic fields.Comment: 15 pages, dirac-electron example has been rewritte

Second Law Induced Existence Conditions for Isothermal 2-Phase Region Cyclic Processes in Binary Mixtures

Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.Conditions describing the behaviour of the kink of isobars at the dew line in v-x-phase diagrams of binary mixtures are proved using the second law. These conditions are interesting in connection to the compatibility of Serogodsky's and van Platen's cycles with the second law of thermodynamics

Variational Principles in Thermodynamics

Instead of equations of motion, variational principles are often used for describing the dynamical behavior of a system. If the equations of motion are variational self-adjoint, the variational principle is equivalent to the equations of motion, because those are given by the Euler-Lagrange equations which belong to the variational principle. If the equations of motion are not variational self-adjoint -as it is the general case in thermodynamics- procedures are discussed to obtain also in these cases a variational problem. Because of lack of variational self-adjointness these variational problems cannot be true ones, they are non-Hamiltonian. By presupposing suflicient conditions an evolution criterion can be derived from the Second Law which results in a Hamiltonian variational principle, also in thermodynamics