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

A PHENOMENOLOGICAL FOUNDATION OF NON-LINEAR OC-RECIPROCAL RELATIONS (IRREVERSIBLE THERMODYNAMICS APPROACH)

Onsager-Casimir reciprocal relations are phenomenologically derived by considering the reversal of so-called rm-parameters. These parameters are defined as being odd under time reversal, if the force densities remain invariant. The reversal of the rm-parameters transforms to an existing process, whereas the time reversal itself is different from the reversal of the rm-parameters and transforms to a macroscopically non-existing process. The derivation of the reciprocal relations needs the second law and the axiom, that the reversal of the rm-parameters induces not only a transformation of the coordinates of thermodynamic forces and fluxes

Non-equilibrium critical behavior : An extended irreversible thermodynamics approach

Critical phenomena in non-equilibrium systems have been studied by means of a wide variety of theoretical and experimental approaches. Mode-coupling, renormalization group, complex Lie algebras and diagrammatic techniques are some of the usual theoretical tools. Experimental studies include light and inelastic neutron scattering, X-ray photon correlation spectroscopy, microwave interferometry and several other techniques. Nevertheless no conclusive reatment has been developed from the basic principles of a thermodynamic theory of irreversible processes. We have developed a formalism in which we obtain correlation functions as field averages of the associated functions. By applying such formalism we attempt to find out if the resulting correlation functions will inherit the mathematical properties (integrability, generalized homogeneity, scaling laws) of its parent potentials, and we will also use these correlation functions to study the behavior of macroscopic systems far from equilibrium, specially in the neighborhood of critical points or dynamic phase transitions. As a working example we will consider the mono-critical behavior of a non-equilibrium binary fluid mixture close to its consolute point.Comment: 23 pages, 3 figures, 1 tabl

Mesoscopic continuum mechanics applied to liquid crystals

Beyond the usual 5-field theory (basic fields: mass density, velocity, internal energy), additional variables are needed for the unique description of complex media. Beside the conventional method of introducing additional fields by their balances, an other procedure, the mesoscopic theory, is here discussed and applied to liquid crystals

Changing the Observer and Moving Materials in Continuum Physics: Objectivity and Frame-Indifference

Because one has to distinguish between changing the observer and changing the motion of a material with respect to a standard frame of reference, objectivity and material frame indifference are of different kind and have to be redefined. Besides objectivity and observer invariance of the balance and constitutive equations, the concept of standard frame dependence is introduced. The objectivity of time derivative operators is investigated with the result that the material time derivative is observer-independent. Although objective constitutive properties are standard frame dependent in general, representation theorems, and therefore the reduced forms of the constitutive equations remain still valid. A remark on non-objective force densities and inertial systems is made

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