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Entropy
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Thermodynamic Constitutive Theory and Its Application
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Thermodynamic Constitutive Theory and Its Application

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Thermodynamics".

Deadline for manuscript submissions: closed (30 January 2024) | Viewed by 6171

Special Issue Editors

Prof. Dr. Christina Papenfuss

E-Mail Website
Guest Editor
Hochschule für Technik und Wirtschaft Berlin, University of Applied Sciences, 12459 Berlin, Germany
Interests: constitutive theory: exploitation of the dissipation inequality; complex materials: mesoscopic and macroscopic theory of liquid crystals, fiber suspensions, mixtures, ferrofluids and others; internal variables and order parameters and their dynamics
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Wolfgang Muschik

E-Mail Website
Guest Editor
Institut für Theoretische Physik, Technische Universität Berlin, 10623 Berlin, Germany
Interests: foundations of non-equilibrium-thermodynamics; quantum thermodynamics; relativistic thermodynamics; thermodynamic of discrete systems; continuum physics and constitutive theory; liquid crystals
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

We invite you to contribute to the Special Issue “Thermodynamic Constitutive Theory and Its Application”.

More than half a century has passed since the foundation of Thermodynamics of Irreversible Processes by Onsager [1, 2], Meixner [3], Prigogine [4] and others, and the foundation of Rational Thermodynamics by Truesdell, Noll [5] and others, and there are still open questions about the role of the Second Law of Thermodynamics in constitutive theory and the method of exploiting the implications of the Second Law. Two examples are hereby mentioned: the question arises when exploiting the dissipation inequality as to whether accelerations should be included in the state space, and, in the case of higher gradient materials, the question remains as to whether derivatives of balance equations need to be taken into account as constraints. The range of applications of thermodynamic constitutive theory is broad and covers, for example, complex materials also including internal processes such as chemical reactions, electromagnetic materials, heat conduction, higher gradient materials and materials for use in engineering applications such as fluids, steel and wood. The strict application of thermodynamic constitutive theory in a relativistic framework, for quantum systems or in stochastic thermodynamics, is still under discussion.

Contributions to fundamental aspects, methods and concepts, as well as applications of phenomenological thermodynamic constitutive theory in all branches of physics, engineering and material science, are welcome.

References

[1] L. Onsager. Reciprocal Relations in Irreversible Processes I. Phys. Rev., 37:405–426, 1931.

[2] L. Onsager. Reciprocal Relations in Irreversible Processes II. Phys. Rev., 38:2265–2279, 1931.

[3] J. Meixner. Zur Thermodynamik der Thermodiffusion. Annalen der Physik, 431(5):333–356, 1941.

[4] I. Prigogine. Introduction to Thermodynamics of Irreversible Processes. Interscience, New York, 1961.

[5] C. Truesdell and W. Noll. The Non-Linear Field Theories of Mechanics. Springer Verlag, Berlin-Heidelberg-New York, 1965. Handbuch der Physik, III/3.

Prof. Dr. Christina Papenfuss
Prof. Dr. Wolfgang Muschik
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Published Papers (7 papers)

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Research

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18 pages, 324 KiB  
Article
Interpretation of Second Law of Thermodynamics in Extended Procedures for the Exploitation of the Entropy Inequality: Korteweg Fluids and Strain-Gradient Elasticity as Examples
by Vito Antonio Cimmelli
Entropy 2024, 26(4), 293; https://doi.org/10.3390/e26040293 - 27 Mar 2024
Viewed by 385
Abstract
In continuum physics the dissipation principle, first proposed by Coleman and Noll in 1963, regards second law of thermodynamics as a unilateral differential constraint on the constitutive equations. In 1996, Muschik and Ehrentraut provided a rigorous proof of such an approach under the [...] Read more.
In continuum physics the dissipation principle, first proposed by Coleman and Noll in 1963, regards second law of thermodynamics as a unilateral differential constraint on the constitutive equations. In 1996, Muschik and Ehrentraut provided a rigorous proof of such an approach under the assumption that, at an arbitrary instant, t0, in an arbitrary point, P0, of a continuous system, the entropy production is zero if, and only if, P0 is in thermodynamic equilibrium. In 2022, Cimmelli and Rogolino incorporated such an assumption in a more general formulation of the second law of thermodynamics. In this paper, we prove that the same conclusions hold if both the fundamental balance laws and their gradients are substituted into the entropy inequality. Such a methodology is applied to analyze the strain-gradient elasticity. Full article
(This article belongs to the Special Issue Thermodynamic Constitutive Theory and Its Application)
21 pages, 422 KiB  
Article
Non-Local Vectorial Internal Variables and Generalized Guyer-Krumhansl Evolution Equations for the Heat Flux
by Liliana Restuccia and David Jou
Entropy 2023, 25(9), 1259; https://doi.org/10.3390/e25091259 - 24 Aug 2023
Viewed by 757
Abstract
In this paper, we ask ourselves how non-local effects affect the description of thermodynamic systems with internal variables. Usually, one assumes that the internal variables are local, but that their evolution equations are non-local, i.e., for instance, that their evolution equations contain non-local [...] Read more.
In this paper, we ask ourselves how non-local effects affect the description of thermodynamic systems with internal variables. Usually, one assumes that the internal variables are local, but that their evolution equations are non-local, i.e., for instance, that their evolution equations contain non-local differential terms (gradients, Laplacians) or integral terms with memory kernels. In contrast to this typical situation, which has led to substantial progress in several fields, we ask ourselves whether in some cases it would be convenient to start from non-local internal variables with non-local evolution equations. We examine this point by considering three main lengths: the observation scale R defining the elementary volumes used in the description of the system, the mean free path l of the microscopic elements of the fluid (particles, phonons, photons, and molecules), and the overall characteristic size L of the global system. We illustrate these ideas by considering three-dimensional rigid heat conductors within the regime of phonon hydrodynamics in the presence of thermal vortices. In particular, we obtain a generalization of the Guyer–Krumhansl equation, which may be of interest for heat transport in nanosystems or in systems with small-scale inhomogeneities. Full article
(This article belongs to the Special Issue Thermodynamic Constitutive Theory and Its Application)
21 pages, 366 KiB  
Article
Thermodynamics of Composition Graded Thermoelastic Solids
by Vito Antonio Cimmelli
Entropy 2023, 25(7), 1084; https://doi.org/10.3390/e25071084 - 19 Jul 2023
Viewed by 741
Abstract
We propose a thermodynamic model describing the thermoelastic behavior of composition graded materials. The compatibility of the model with the second law of thermodynamics is explored by applying a generalized Coleman–Noll procedure. For the material at hand, the specific entropy and the stress [...] Read more.
We propose a thermodynamic model describing the thermoelastic behavior of composition graded materials. The compatibility of the model with the second law of thermodynamics is explored by applying a generalized Coleman–Noll procedure. For the material at hand, the specific entropy and the stress tensor may depend on the gradient of the unknown fields, resulting in a very general theory. We calculate the speeds of coupled first- and second-sound pulses, propagating either trough nonequilibrium or equilibrium states. We characterize several different types of perturbations depending on the value of the material coefficients. Under the assumption that the deformation of the body can produce changes in its stoichiometry, altering locally the material composition, the possibility of propagation of pure stoichiometric waves is pointed out. Thermoelastic perturbations generated by the coupling of stoichiometric and thermal effects are analyzed as well. Full article
(This article belongs to the Special Issue Thermodynamic Constitutive Theory and Its Application)
11 pages, 275 KiB  
Article
A Special Relativistic Exploitation of the Second Law of Thermodynamics and Its Non-Relativistic Limit
by Christina Papenfuss
Entropy 2023, 25(6), 952; https://doi.org/10.3390/e25060952 - 17 Jun 2023
Viewed by 770
Abstract
A thermodynamic process is a solution of the balance equations fulfilling the second law of thermodynamics. This implies restrictions on the constitutive relations. The most general way to exploit these restrictions is the method introduced by Liu. This method is applied here, in [...] Read more.
A thermodynamic process is a solution of the balance equations fulfilling the second law of thermodynamics. This implies restrictions on the constitutive relations. The most general way to exploit these restrictions is the method introduced by Liu. This method is applied here, in contrast to most of the literature on relativistic thermodynamic constitutive theory, which goes back to a relativistic extension of the Thermodynamics of Irreversible Processes. In the present work, the balance equations and the entropy inequality are formulated in the special relativistic four-dimensional form for an observer with four-velocity parallel to the particle current. The restrictions on constitutive functions are exploited in the relativistic formulation. The domain of the constitutive functions, the state space, is chosen to include the particle number density, the internal energy density, the space derivatives of these quantities, and the space derivative of the material velocity for a chosen observer. The resulting restrictions on constitutive functions, as well as the resulting entropy production are investigated in the non-relativistic limit, and relativistic correction terms of the lowest order are derived. The restrictions on constitutive functions and the entropy production in the low energy limit are compared to the results of an exploitation of the non-relativistic balance equations and entropy inequality. In the next order of approximation our results are compared to the Thermodynamics of Irreversible Processes. Full article
(This article belongs to the Special Issue Thermodynamic Constitutive Theory and Its Application)
26 pages, 374 KiB  
Article
Constitutive Modeling with Single and Dual Internal Variables
by Arkadi Berezovski
Entropy 2023, 25(5), 721; https://doi.org/10.3390/e25050721 - 26 Apr 2023
Viewed by 975
Abstract
Phenomenological constitutive models with internal variables have been applied for a wide range of material behavior. The developed models can be classified as related to the single internal variable formalism based on the thermodynamic approach by Coleman and Gurtin. The extension of this [...] Read more.
Phenomenological constitutive models with internal variables have been applied for a wide range of material behavior. The developed models can be classified as related to the single internal variable formalism based on the thermodynamic approach by Coleman and Gurtin. The extension of this theory to so-called dual internal variables opens up new avenues for the constitutive modeling of macroscopic material behavior. This paper reveals the distinction between constitutive modeling with single and dual internal variables using examples of heat conduction in rigid solids, linear thermoelasticity, and viscous fluids. A thermodynamically consistent framework for treating internal variables with as little a priori knowledge as possible is presented. This framework is based on the exploitation of the Clausius–Duhem inequality. Since the considered internal variables are “observable but not controllable”, only the Onsagerian procedure with the use of the extra entropy flux is appropriate for the derivation of evolution equations for internal variables. The key distinctions between single and dual internal variables are that the evolution equations are parabolic in the case of a single internal variable and hyperbolic if dual internal variables are employed. Full article
(This article belongs to the Special Issue Thermodynamic Constitutive Theory and Its Application)

Review

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50 pages, 3321 KiB  
Review
Non-Equilibrium Thermodynamics of Heat Transport in Superlattices, Graded Systems, and Thermal Metamaterials with Defects
by David Jou and Liliana Restuccia
Entropy 2023, 25(7), 1091; https://doi.org/10.3390/e25071091 - 20 Jul 2023
Cited by 2 | Viewed by 1148
Abstract
In this review, we discuss a nonequilibrium thermodynamic theory for heat transport in superlattices, graded systems, and thermal metamaterials with defects. The aim is to provide researchers in nonequilibrium thermodynamics as well as material scientists with a framework to consider in a systematic [...] Read more.
In this review, we discuss a nonequilibrium thermodynamic theory for heat transport in superlattices, graded systems, and thermal metamaterials with defects. The aim is to provide researchers in nonequilibrium thermodynamics as well as material scientists with a framework to consider in a systematic way several nonequilibrium questions about current developments, which are fostering new aims in heat transport, and the techniques for achieving them, for instance, defect engineering, dislocation engineering, stress engineering, phonon engineering, and nanoengineering. We also suggest some new applications in the particular case of mobile defects. Full article
(This article belongs to the Special Issue Thermodynamic Constitutive Theory and Its Application)
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8 pages, 272 KiB  
Tutorial
Second Law and Its Amendment: The Axiom of No-Reversible Directions Revisited
by Wolfgang Muschik
Entropy 2023, 25(8), 1226; https://doi.org/10.3390/e25081226 - 17 Aug 2023
Cited by 2 | Viewed by 680
Abstract
A toy model is used to describe the following steps to achieve the no-reversible-direction axiom in a tutorial manner: (i) choose a state space results in the balance equations on state space which are linear in the process directions, (ii) avoid a reversible [...] Read more.
A toy model is used to describe the following steps to achieve the no-reversible-direction axiom in a tutorial manner: (i) choose a state space results in the balance equations on state space which are linear in the process directions, (ii) avoid a reversible process direction that cannot be generated via a combination of non-reversible ones, (iii) process directions that are in the kernel of the balance equations and do not enter the entropy production. The Coleman–Mizel formulation of the second law and the Liu relations follow immediately. Full article
(This article belongs to the Special Issue Thermodynamic Constitutive Theory and Its Application)
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