The relation between relativistic and non-relativistic continuum thermodynamics

Schellstede, Gerold Oltman; Borzeszkowski, H.‐H. von; Chrobok, Thoralf; Muschik, W.

doi:10.1007/s10714-013-1640-8

Cited by 9 publications

(9 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Equilibrium is defined by equilibrium conditions which are divided into necessary and supplementary ones [11,12,36]. The necessary equilibrium conditions are given by vanishing entropy production, vanishing entropy flux density and vanishing entropy supply.…”

Section: Discussionmentioning

confidence: 99%

Covariant Relativistic Non-Equilibrium Thermodynamics of Multi-Component Systems

Muschik

2019

Entropy

View full text Add to dashboard Cite

Keywords General-covariant multi-component systems · Entropy Identity · Entropy balance of a component of the mixture · Entropy balance of the mixture · Multi-temperature relaxation · Equilibrium conditions: 4-temperature's Killing relation · Extended Belinfante/Rosenfeld procedure · 2-component plain-ghost mixture Abstract 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. member of the mixture is investigated. Thus, each component of the mixture is equipped with its own temperature, pressure, energy and mass density which all together generate the corresponding quantities of the mixture.Considering a multi-component system, three items have to be distinguished: one component as a member of the multi-component system which interacts with all the other components of the system, the same component as a free 1-component system separated from the multi-component system and finally the multi-component system itself as a mixture which is composed of its components. Here, all three items are discussed in a covariant-relativistic framework. For finding out the entropy-flux, -supply, -production and -density, a special tool is used: the entropy identity which constrains the possibility of an arbitrary choice of these quantities [9,10,11,12]. Following J. Meixner and J.U. Keller that entropy in non-equilibrium cannot be defined unequivocally [13,14,15,16,17], the entropy identity is only an (well set up) ansatz for constructing a non-equilibrium entropy and further corresponding quantities. This fact in mind, a specific entropy and the corresponding Gibbs and Gibbs-Duhem equations are derived. The definition of the rest mass flux densities, of the energy and momentum balances and of the corresponding balances of the spin tensor are taken into account as contraints in the entropy identity by introducing fields of Lagrange multipliers. The physical dimensions of these factors allow to determine their physical meaning.Equilibrium is defined by equilibrium conditions which are divided into basic ones given by vanishing entropy-flux, -supply and -production and into supplementary ones such as vanishing diffusion flux, vanishing heat flux and zero rest mass production [11,12]. The Killing relation of the 4-temperature concerning equilibrium is shortly d...

show abstract

Section: Discussionmentioning

confidence: 99%

Covariant Relativistic Non-Equilibrium Thermodynamics of Multi-Component Systems

Muschik

2019

Entropy

View full text Add to dashboard Cite

show abstract

“…In analogy to the approach in [13] we make a series expansion with respect to ǫ ∼ F mn /A to tackle the question under which conditions a theory of Plebańaki's class is compatible with Maxwell's theory as a weak field limit and to derive post-Maxwellian terms for the field equations. To do so some series expansions are needed which will be done next.…”

Section: Series Expansionsmentioning

confidence: 99%

On the weak‐field approximation of nonlinear vacuum electrodynamics of the Plebański class

Schellstede

2017

Annalen der Physik

View full text Add to dashboard Cite

Plebański's class of nonlinear vacuum electrodynamics is considered, which is for several reasons of interest at the present time. In particular, the question is answered under which circumstances Maxwell's original field equations are recovered approximately and which 'post-Maxwellian' effects could arise. To this end, a weak field approximation method is developed, allowing to calculate 'post-Maxwellian' corrections up to Nth order. In some respect, this is analogue of determining 'post-Newtonian' corrections from relativistic mechanics by a low velocity approximation. As a result, we got a series of linear field equations that can be solved order by order. In this context, the solutions of the lower orders occur as source terms inside the higher order field equations and represent a 'post-Maxwellian' self-interaction of the electromagnetic field, which increases order by order. It becomes apparent that one has to distinguish between problems with and without external source terms because without sources also high frequency solutions can be approximately described by Maxwell's original equations. The higher order approximations, which describe 'post-Maxwellian' effects, can give rise to experimental tests of Plebańksi's class. Finally, two boundary value problems are discussed to have examples at hand.

show abstract

“…The reformulation of the dynamic equations ( 32) - (35) in terms of the space-times (5) and some tedious algebra brings us to a set of ordinary differential equations which can be solved analytically.…”

Section: A Solutions Of the Propagation Equationsmentioning

confidence: 99%

“…and ( 24), the tetrad formulations for the propagation equations of the heat-flux (34) and the anisotropic pressure (35) together with the kinematic quantities ( 24) -( 26) yield the following integrable partial differential equations:…”

Section: A Solutions Of the Propagation Equationsmentioning

confidence: 99%

See 1 more Smart Citation

Non-Perfect-Fluid Space-Times in Thermodynamic Equilibrium and Generalized Friedmann Equations

2016

View full text Add to dashboard Cite

We determine the energy-momentum tensor of non-perfect fluids in thermodynamic equilibrium. To this end, we derive the constitutive equations for energy density, isotropic and anisotropic pressure as well as for heat-flux from the corresponding propagation equations and by drawing on Einstein's equations. Following Obukhov at this, we assume the corresponding space-times to be conformstationary and homogeneous. This procedure provides these quantities in closed form, i.e., in terms of the structure constants of the three-dimensional isometry group of homogeneity and, respectively, in terms of the kinematical quantities expansion, rotation and acceleration. In particular, we find a generalized form of the Friedmann equations. As special cases we recover Friedmann and Gödel models as well as non-tilted Bianchi solutions with anisotropic pressure. All of our results are derived without assuming any equations of state or other specific thermodynamic conditions a priori. For the considered models, results in literature are generalized to rotating fluids with dissipative fluxes.PACS numbers: 04.20.-q, 04.40.-b, 47.75.+f, 98.80.Jk * konscha@physik.tu-berlin.de † borzeszk@mailbox.tu-berlin.de ‡ tchrobok@mailbox.tu-berlin.de 1 We emphasize that we approach this without any specific thermodynamic conditions as done for instance in [16], i. e., we refrain from applying linear or extended thermodynamics.

show abstract

The relation between relativistic and non-relativistic continuum thermodynamics

Cited by 9 publications

References 26 publications

Covariant Relativistic Non-Equilibrium Thermodynamics of Multi-Component Systems

Covariant Relativistic Non-Equilibrium Thermodynamics of Multi-Component Systems

On the weak‐field approximation of nonlinear vacuum electrodynamics of the Plebański class

Non-Perfect-Fluid Space-Times in Thermodynamic Equilibrium and Generalized Friedmann Equations

Contact Info

Product

Resources

About