Comment on: I-Shih Liu: Constitutive theory of anisotropic rigid heat conductors

In I-Shih Liu's paper \C{1}, the compatibility of anisotropy and material frame indifference of a rigid heat conductor is investigated. For this purpose, the deformation gradient is introduced into the domain of the constitutive mapping. Because of the presupposed rigidity, the deformation gradient is here represented by an orthogonal tensor. The statement, that the usual procedure -- not to introduce the deformation gradient into the state space of rigid heat conductors -- causes isotropy because of the material frame indifference, is misleading.Comment: 8 page

Covariant Relativistic Non-Equilibrium Thermodynamics of Multi-Component Systems

Non-equilibrium and equilibrium thermodynamics of an interacting component in a relativistic multi-component system is discussed covariantly by exploiting an entropy identity. The special case of the corresponding free component is considered. Equilibrium conditions and especially the multi-component Killing relation of the 4-temperature are discussed. Two axioms characterize the mixture: additivity of the energy momentum tensors and additivity of the 4-entropies of the components generating those of the mixture. The resulting quantities of a single component and of the mixture as a whole, energy, energy flux, momentum flux, stress tensor, entropy, entropy flux, supply and production are derived. Finally, a general relativistic 2-component mixture is discussed with respect to their gravitation generating energy–momentum tensors

Entropy Production and Equilibrium Conditions of General-Covariant Spin Systems

In generalizing the special-relativistic one-component version of Eckart's continuum thermodynamics to general-relativistic space-times with Riemannian or post-Riemannian geometry, we consider the entropy production and other themodynamical quantities such as the entropy flux and the Gibbs fundamental equation. We discuss equilibrium conditions in gravitational theories which are based on such geometries. In particular, thermodynamic implications of the non-symmetry of the energy-momentum tensor and the related spin balance equations are investigated, also for the special case of General Relativity.Comment: General-covariant spin systems are carefully discussed in the framework of non-equlibrium thermodynamics starting out with an already published entropy identit

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

Book Review: Physics of Self-Organization and Evolution, Wiley-VCH, Weinheim, 2011, ISBN 978-3-527-40963-1, by Rainer Feistel and Werner Ebeling

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

Irreversibility and Second Law

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.According to M. Eigen there are two reasons for irreversibility: weak and strict temporality. Measures for irreversibility are defined by different formulations of the 2nd law which can be divided into two classes: the more general in time integrated formulations as Clausius' inequality and the more special in time local formulations as the non-negativity of the entropy production density. The logical relations between eight different formulations of the 2nd law are investigated and discussed