Special Issue "Second Law: Survey and Application"

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

Deadline for manuscript submissions: closed (31 October 2019).

Special Issue Editors

Prof. Dr. Wolfgang Muschik
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Guest Editor
Technische Universität Berlin, 10623 Berlin, Germany
Interests: non-equilibrium thermodynamics: Discrete systems, field formulation, 2nd law; mesoscopic theory: Liquid crystals, order parameters; constitutive theory: Exploitation of the dissipation inequality, moving materials; evolution criteria; variational principles; relativistic thermodynamics
Prof. Dr. Christina Papenfuss
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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 Issue Information

Dear Colleagues,

This is an invitation to contribute to the Special Issue "Second Law: Survey and Application". The Second Law launches with two verbal formulations concerning irreversible cyclic processes of discrete systems: The principle of Kelvin (1882) and that of Clausius (1861, 1865). In the meantime, there are "as many formulations of the Second Law as there are authors" (Hutter 1977). Nevertheless, Clausius' extended inequality of irreversible processes in open discrete systems is still today a foundation of the Second Law, if it is formulated by use of time differentials. Two other versions of the Second Law are mentioned, that of Caratheodory (1909) in Bernstein's modification (1960) and that of Sears/Kestin (1963/1970). Essential tools were developed which improve our understanding of discrete systems interacting with their environment: Contact quantities belonging to the discrete system which replace controlling items of the environment; accompanying processes which elucidate the meaning of reversible processes; extension of the Second Law to negative absolute temperatures.

Classical non-linear field theories contain balance equations belonging to physically relevant quantities, such as entropy (of course in non-equilibrium). The entropy balance equation connects the time derivative of the entropy density with the entropy flux density, the entropy supply and the entropy production density. Except of the entropy supply, these quantities are constitutive fields, that means, their special shape depends on the material in consideration. In addition to the entropy balance, the balances of mass, energy and momentum and, if necessary, those of spin, internal variables and other ones for complex materials have to be taken into account. These balance equations form a system of underdetermined differential equations which has to be supplemented by constitutive equations. Dependent on the material, a state space has to be chosen which represents the domain of all fields generating a well posed system of differential equations whose solution is wanted under the constraint that the field of the entropy production density is not negative. This constraint represents the Second Law of the thermodynamical field theory.

The coinage of thermodynamical field theories is many-sided: Different state spaces are used in irreversible thermodynamics, extended thermodynamics, higher gradient and weakly nonlocal thermodynamics and thermodynamics of heat conduction, of surfaces and interfaces, and of complex systems; different exploitation procedures of the non-negative entropy production density in extended and irreversible extended thermodynamics; and different standards in relativistic thermodynamics.

Evolution criteria and GENERIC are other theoretical approaches to thermodynamics apart from thermodynamical field theories. The Second Law plays a central role in all phenomenological thermodynamical theories because it describes the macroscopic Zeitpfeil of the considered system. But on a microscopic stochastic level, there are processes of temporal negative process entropy (Jarzynski 1977), denoted as "violations" of the Second Law, a name which is not correct because the (macroscopic) Second Law is also valid in stochastic thermodynamics as a statistical mean–value.

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

Manuscript Submission Information

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Keywords

  • different formulations of the Second Law
  • continuum thermodynamics and discrete systems
  • constitutive theory: methods of exploiting the dissipation inequality
  • irreversible thermodynamics
  • extended thermodynamics
  • higher gradient theories
  • weakly nonlocal thermodynamics
  • constitutive theory of heat conduction
  • complex systems
  • internal variables
  • evolution criteria and GENERIC
  • Second Law in stochastic and relativistic thermodynamics

Published Papers (7 papers)

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Research

Open AccessArticle
On the Impossibility of First-Order Phase Transitions in Systems Modeled by the Full Euler Equations
Entropy 2019, 21(11), 1039; https://doi.org/10.3390/e21111039 - 25 Oct 2019
Abstract
Liquid–vapor flows exhibiting phase transition, including phase creation in single-phase flows, are of high interest in mathematics, as well as in the engineering sciences. In two preceding articles the authors showed on the one hand the capability of the isothermal Euler equations to [...] Read more.
Liquid–vapor flows exhibiting phase transition, including phase creation in single-phase flows, are of high interest in mathematics, as well as in the engineering sciences. In two preceding articles the authors showed on the one hand the capability of the isothermal Euler equations to describe such phenomena (Hantke and Thein, arXiv, 2017, arXiv:1703.09431). On the other hand they proved the nonexistence of certain phase creation phenomena in flows governed by the full system of Euler equations, see Hantke and Thein, Quart. Appl. Math. 2015, 73, 575–591. In this note, the authors close the gap for two-phase flows by showing that the two-phase flows considered are not possible when the flow is governed by the full Euler equations, together with the regular Rankine-Hugoniot conditions. The arguments rely on the fact that for (regular) fluids, the differences of the entropy and the enthalpy between the liquid and the vapor phase of a single substance have a strict sign below the critical point. Full article
(This article belongs to the Special Issue Second Law: Survey and Application)
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Open AccessArticle
Covariant Relativistic Non-Equilibrium Thermodynamics of Multi-Component Systems
Entropy 2019, 21(11), 1034; https://doi.org/10.3390/e21111034 - 24 Oct 2019
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Second Law: Survey and Application)
Open AccessArticle
A Thermodynamic Constitutive Model for Saturated Sand
Entropy 2019, 21(2), 136; https://doi.org/10.3390/e21020136 - 01 Feb 2019
Abstract
This paper establishes a non-equilibrium thermodynamic constitutive model that can predict the undrained shear behavior of saturated sand. Starting from the basic laws of thermodynamics, the model does not require the classical concepts in elasto-plastic models, such as the yield function, the flow [...] Read more.
This paper establishes a non-equilibrium thermodynamic constitutive model that can predict the undrained shear behavior of saturated sand. Starting from the basic laws of thermodynamics, the model does not require the classical concepts in elasto-plastic models, such as the yield function, the flow rule, and the hardening rule. It is also different from the existing thermodynamic constitutive models in soil mechanics literatures. The model does not use a complex nonlinear elastic potential as usually and introduces a coupling energy dissipative mechanism between the viscosity and elasticity relaxation, which is essential in granular materials. Then this model was used to simulate the undrained shear test of Toyoura sand. The model can predict the critical state, dilatancy-contraction and hardening-softening characteristics of sand during undrained triaxial shearing. Full article
(This article belongs to the Special Issue Second Law: Survey and Application)
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Open AccessArticle
Optimization and Entropy Production: Application to Carnot-Like Refrigeration Machines
Entropy 2018, 20(12), 953; https://doi.org/10.3390/e20120953 - 11 Dec 2018
Cited by 1
Abstract
Several optimization models of irreversible reverse cycle machines have been developed based on different optimization criteria in the literature, most of them using linear heat transfer laws at the source and sink. This raises the issue how close to actual operation conditions they [...] Read more.
Several optimization models of irreversible reverse cycle machines have been developed based on different optimization criteria in the literature, most of them using linear heat transfer laws at the source and sink. This raises the issue how close to actual operation conditions they are, since the heat transfer law on the phase-change processes is dependent on ΔT3. This paper addresses this issue by proposing a general model for study and optimization of thermal machines with two heat reservoirs applied to a Carnot-like refrigerator, with non-linear heat transfer laws and internal and external irreversibility. The optimization was performed using First and Second Law of Thermodynamics and the Lagrange multipliers method. Thus, several constraints were imposed to the system, also different objective functions were considered, allowing finding the optimum operating conditions, as well as the limited variation ranges of the system parameters. Results show that the nature of the heat transfer laws affects the optimum values of system parameters for obtaining maximum performances and also their magnitude. Sensitivity studies with respect to system several parameters are presented. The results contribute to the understanding of the system limits in operation under different constraints and allow choosing the most convenient variables in given circumstances. Full article
(This article belongs to the Special Issue Second Law: Survey and Application)
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Open AccessArticle
Triphase Separation of a Ternary Symmetric Highly Viscous Mixture
Entropy 2018, 20(12), 936; https://doi.org/10.3390/e20120936 - 06 Dec 2018
Abstract
We discuss numerical results of diffusion-driven separation into three phases of a symmetric, three-component highly viscous liquid mixture after an instantaneous quench from the one-phase region into an unstable location within the tie triangle of its phase diagram. Our theoretical approach follows a [...] Read more.
We discuss numerical results of diffusion-driven separation into three phases of a symmetric, three-component highly viscous liquid mixture after an instantaneous quench from the one-phase region into an unstable location within the tie triangle of its phase diagram. Our theoretical approach follows a diffuse-interface model of partially miscible ternary liquid mixtures that incorporates the one-parameter Margules correlation as a submodel for the enthalpic (so-called excess) component of the Gibbs energy of mixing, while its nonlocal part is represented based on a square-gradient (Cahn–Hilliard-type) modeling assumption. The governing equations for this phase-field ternary mixture model are simulated in 3D, showing the segregation kinetics in terms of basic segregation statistics, such as the integral scale of the pair-correlation function and the separation depth for each component. Based on the temporal evolution of the integral scales, phase separation takes place via the simultaneous growth of three phases up until a symmetry-breaking event after which one component continues to separate quickly, while phase separation for the other two seems to be delayed. However, inspection of the separation depths reveals that there can be no symmetry among the three components at any instant in time during a triphase segregation process. Full article
(This article belongs to the Special Issue Second Law: Survey and Application)
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Open AccessArticle
Magnetic Contribution to the Seebeck Effect
Entropy 2018, 20(12), 912; https://doi.org/10.3390/e20120912 - 30 Nov 2018
Abstract
The Seebeck effect is derived within the thermodynamics of irreversible processes when the generalized forces contain the magnetic term M B . This term appears in the formalism when the magnetic field is treated as a state variable. Two subsystems are considered, [...] Read more.
The Seebeck effect is derived within the thermodynamics of irreversible processes when the generalized forces contain the magnetic term M B . This term appears in the formalism when the magnetic field is treated as a state variable. Two subsystems are considered, one representing atomic magnetic moments, and the other, mobile charges carrying a magnetic dipole moment. A magnetic contribution to the Seebeck coefficient is identified, proportional to the logarithmic derivative of the magnetization with respect to temperature. A brief review of experimental data on magneto-thermopower in magnetic metals illustrates this magnetic effect on thermally-driven charge transport. Full article
(This article belongs to the Special Issue Second Law: Survey and Application)
Open AccessArticle
Second Law and Non-Equilibrium Entropy of Schottky Systems—Doubts and Verification–
Entropy 2018, 20(10), 740; https://doi.org/10.3390/e20100740 - 28 Sep 2018
Cited by 1
Abstract
Meixner’s historical remark in 1969 “... it can be shown that the concept of entropy in the absence of equilibrium is in fact not only questionable but that it cannot even be defined....” is investigated from today’s insight. Several statements—such as the three [...] Read more.
Meixner’s historical remark in 1969 “... it can be shown that the concept of entropy in the absence of equilibrium is in fact not only questionable but that it cannot even be defined....” is investigated from today’s insight. Several statements—such as the three laws of phenomenological thermodynamics, the embedding theorem and the adiabatical uniqueness—are used to get rid of non-equilibrium entropy as a primitive concept. In this framework, Clausius inequality of open systems can be derived by use of the defining inequalities which establish the non-equilibrium quantities contact temperature and non-equilibrium molar entropy which allow to describe the interaction between the Schottky system and its controlling equilibrium environment. Full article
(This article belongs to the Special Issue Second Law: Survey and Application)
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