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Simulation with Entropy Thermodynamics

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

Deadline for manuscript submissions: closed (30 September 2020) | Viewed by 41390

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Special Issue Editor

Prof. Dr. Christophe Goupil

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Guest Editor

CNRS, UMR 8236-LIED, Université Paris Cité, 75013 Paris, France
Interests: out-of-equilibrium thermodynamics; solid-state physics; thermoelectricity; living systems; thermodynamics optimization; network thermodynamics; ecological economics
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Special Issue Information

Dear Colleagues

Energy conversion processes are at the heart of many of the challenges currently faced by our communities. Among them, the issues of entropy production and dissipation are particularly important. Not generally adhering to variational principles, the study of these processes remains an area that is not fully explored. The development of tools for simulating entropic processes, based on proven theoretical foundations, is a challenge, from both a fundamental and an applied point of view.

Among the issues discussed are those concerning the operating points of the processes, somewhere between minimizing and maximizing entropy production, or the famous principle of maximum power.

This Special Issue aims to address a broad audience, covering the sciences of condensed matter by including quantum aspects, the sciences of soft matter by including stochastic processes, and the sciences of life by including the optimization of unbalanced behaviors. In addition, a place will also be given to the economic sciences in their ecological dimension.

By considering this topic from multiple perspectives relating physical systems to engineering, living systems, or fundamental processes, this special volume aims to provide the reader with an overview of the associated issues, which are addressed by simulations.

The main topics of this Special Issue include (but not limited to):

* Entropy production, dissipation, and optimization

* Bond-graph and pseudo-bond-graph simulation

* Linear out-of-equilibrium processes

* Far form equilibrium, including large deviation processes

* Quantum Thermodynamics

* Network Thermodynamics

* Stochastic Thermodynamics

* Biological processes

* Entropy and Information

* Ecological Economics

Prof. Dr. Christophe Goupil
Guest Editor

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Keywords

Out-of-equilibrium thermodynamics
Solid-state physics
Quantum thermodynamics
Living systems
Network Thermodynamics
Bond-graph
Ecological Economics.

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Published Papers (11 papers)

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Research

22 pages, 8088 KiB

Open AccessArticle

Geometry Optimization of Thermoelectric Modules: Deviation of Optimum Power Output and Conversion Efficiency

by Mario Wolf, Alexey Rybakov, Richard Hinterding and Armin Feldhoff

Entropy 2020, 22(11), 1233; https://doi.org/10.3390/e22111233 - 29 Oct 2020

Cited by 10 | Viewed by 2561

Abstract

Besides the material research in the field of thermoelectrics, the way from a material to a functional thermoelectric (TE) module comes alongside additional challenges. Thus, comprehension and optimization of the properties and the design of a TE module are important tasks. In this work, different geometry optimization strategies to reach maximum power output or maximum conversion efficiency are applied and the resulting performances of various modules and respective materials are analyzed. A Bi₂Te₃-based module, a half-Heusler-based module, and an oxide-based module are characterized via FEM simulations. By this, a deviation of optimum power output and optimum conversion efficiency in dependence of the diversity of thermoelectric materials is found. Additionally, for all modules, the respective fluxes of entropy and charge as well as the corresponding fluxes of thermal and electrical energy within the thermolegs are shown. The full understanding and enhancement of the performance of a TE module may be further improved. Full article

(This article belongs to the Special Issue Simulation with Entropy Thermodynamics)

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18 pages, 1517 KiB

Open AccessArticle

Discrepancy between Constant Properties Model and Temperature-Dependent Material Properties for Performance Estimation of Thermoelectric Generators

by Prasanna Ponnusamy, Johannes de Boor and Eckhard Müller

Entropy 2020, 22(10), 1128; https://doi.org/10.3390/e22101128 - 4 Oct 2020

Cited by 9 | Viewed by 2109

Abstract

The efficiency of a thermoelectric (TE) generator for the conversion of thermal energy into electrical energy can be easily but roughly estimated using a constant properties model (CPM) developed by Ioffe. However, material properties are, in general, temperature (

T

)-dependent and the [...] Read more.

T

)-dependent and the CPM yields meaningful estimates only if physically appropriate averages, i.e., spatial averages for thermal and electrical resistivities and the temperature average (TAv) for the Seebeck coefficient (

α)

, are used. Even though the use of

α_{TAv}

compensates for the absence of Thomson heat in the CPM in the overall heat balance, we find that the CPM still overestimates performance (e.g., by up to 6% for PbTe) for many materials. The deviation originates from an asymmetric distribution of internally released Joule heat to either side of the TE leg and the distribution of internally released Thomson heat between the hot and cold side. The Thomson heat distribution differs from a complete compensation of the corresponding Peltier heat balance in the CPM. Both effects are estimated quantitatively here, showing that both may reach the same order of magnitude, but which one dominates varies from case to case, depending on the specific temperature characteristics of the thermoelectric properties. The role of the Thomson heat distribution is illustrated by a discussion of the transport entropy flow based on the

α (T)

plot. The changes in the lateral distribution of the internal heat lead to a difference in the heat input, the optimum current and thus of the efficiency of the CPM compared to the real case, while the estimate of generated power at maximum efficiency remains less affected as it is bound to the deviation of the optimum current, which is mostly <1%. This deviation can be corrected to a large extent by estimating the lateral Thomson heat distribution and the asymmetry of the Joule heat distribution. A simple guiding rule for the former is found. Full article

(This article belongs to the Special Issue Simulation with Entropy Thermodynamics)

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13 pages, 2555 KiB

Open AccessArticle

Analysis of Entropy Production in Structured Chemical Reactors: Optimization for Catalytic Combustion of Air Pollutants

by Mateusz Korpyś, Anna Gancarczyk, Marzena Iwaniszyn, Katarzyna Sindera, Przemysław J. Jodłowski and Andrzej Kołodziej

Entropy 2020, 22(9), 1017; https://doi.org/10.3390/e22091017 - 11 Sep 2020

Cited by 5 | Viewed by 2601

Abstract

Optimization of structured reactors is not without some difficulties due to highly random economic issues. In this study, an entropic approach to optimization is proposed. The model of entropy production in a structured catalytic reactor is introduced and discussed. Entropy production due to flow friction, heat and mass transfer and chemical reaction is derived and referred to the process yield. The entropic optimization criterion is applied for the case of catalytic combustion of methane. Several variants of catalytic supports are considered including wire gauzes, classic (long-channel) and short-channel monoliths, packed bed and solid foam. The proposed entropic criterion may indicate technically rational solutions of a reactor process that is as close as possible to the equilibrium, taking into account all the process phenomena such as heat and mass transfer, flow friction and chemical reaction. Full article

(This article belongs to the Special Issue Simulation with Entropy Thermodynamics)

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40 pages, 2031 KiB

Open AccessEditor’s ChoiceArticle

Power Conversion and Its Efficiency in Thermoelectric Materials

by Armin Feldhoff

Entropy 2020, 22(8), 803; https://doi.org/10.3390/e22080803 - 22 Jul 2020

Cited by 24 | Viewed by 3981

Abstract

The basic principles of thermoelectrics rely on the coupling of entropy and electric charge. However, the long-standing dispute of energetics versus entropy has long paralysed the field. Herein, it is shown that treating entropy and electric charge in a symmetric manner enables a simple transport equation to be obtained and the power conversion and its efficiency to be deduced for a single thermoelectric material apart from a device. The material’s performance in both generator mode (thermo-electric) and entropy pump mode (electro-thermal) are discussed on a single voltage-electrical current curve, which is presented in a generalized manner by relating it to the electrically open-circuit voltage and the electrically closed-circuited electrical current. The electrical and thermal power in entropy pump mode are related to the maximum electrical power in generator mode, which depends on the material’s power factor. Particular working points on the material’s voltage-electrical current curve are deduced, namely, the electrical open circuit, electrical short circuit, maximum electrical power, maximum power conversion efficiency, and entropy conductivity inversion. Optimizing a thermoelectric material for different working points is discussed with respect to its figure-of-merit

z T

and power factor. The importance of the results to state-of-the-art and emerging materials is emphasized. Full article

(This article belongs to the Special Issue Simulation with Entropy Thermodynamics)

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8 pages, 1136 KiB

Open AccessEditor’s ChoiceArticle

Entropy of Conduction Electrons from Transport Experiments

by Nicolás Pérez, Constantin Wolf, Alexander Kunzmann, Jens Freudenberger, Maria Krautz, Bruno Weise, Kornelius Nielsch and Gabi Schierning

Entropy 2020, 22(2), 244; https://doi.org/10.3390/e22020244 - 21 Feb 2020

Cited by 5 | Viewed by 4172

Abstract

The entropy of conduction electrons was evaluated utilizing the thermodynamic definition of the Seebeck coefficient as a tool. This analysis was applied to two different kinds of scientific questions that can—if at all—be only partially addressed by other methods. These are the field-dependence of meta-magnetic phase transitions and the electronic structure in strongly disordered materials, such as alloys. We showed that the electronic entropy change in meta-magnetic transitions is not constant with the applied magnetic field, as is usually assumed. Furthermore, we traced the evolution of the electronic entropy with respect to the chemical composition of an alloy series. Insights about the strength and kind of interactions appearing in the exemplary materials can be identified in the experiments. Full article

(This article belongs to the Special Issue Simulation with Entropy Thermodynamics)

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10 pages, 658 KiB

Open AccessEditor’s ChoiceArticle

Thermodynamic and Transport Properties of Equilibrium Debye Plasmas

by Gianpiero Colonna and Annarita Laricchiuta

Entropy 2020, 22(2), 237; https://doi.org/10.3390/e22020237 - 20 Feb 2020

Cited by 6 | Viewed by 3383

Abstract

The thermodynamic and transport properties of weakly non-ideal, high-density partially ionized hydrogen plasma are investigated, accounting for quantum effects due to the change in the energy spectrum of atomic hydrogen when the electron–proton interaction is considered embedded in the surrounding particles. The complexity of the rigorous approach led to the development of simplified models, able to include the neighbor-effects on the isolated system while remaining consistent with the traditional thermodynamic approach. High-density conditions have been simulated assuming particle interactions described by a screened Coulomb potential. Full article

(This article belongs to the Special Issue Simulation with Entropy Thermodynamics)

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9 pages, 566 KiB

Open AccessArticle

The Ohm Law as an Alternative for the Entropy Origin Nonlinearities in Conductivity of Dilute Colloidal Polyelectrolytes

by Ioulia Chikina, Valeri Shikin and Andrey Varlamov

Entropy 2020, 22(2), 225; https://doi.org/10.3390/e22020225 - 17 Feb 2020

Cited by 6 | Viewed by 3011

Abstract

We discuss the peculiarities of the Ohm law in dilute polyelectrolytes containing a relatively low concentration

n_{⊙}

of multiply charged colloidal particles. It is demonstrated that in these conditions, the effective conductivity of polyelectrolyte is the linear function of

n_{⊙}

. [...] Read more.

We discuss the peculiarities of the Ohm law in dilute polyelectrolytes containing a relatively low concentration

n_{⊙}

of multiply charged colloidal particles. It is demonstrated that in these conditions, the effective conductivity of polyelectrolyte is the linear function of

n_{⊙}

. This happens due to the change of the electric field in the polyelectrolyte under the effect of colloidal particle polarization. The proposed theory explains the recent experimental findings and presents the alternative to mean spherical approximation which predicts the nonlinear I–V characteristics of dilute colloidal polyelectrolytes due to entropy changes. Full article

(This article belongs to the Special Issue Simulation with Entropy Thermodynamics)

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20 pages, 620 KiB

Open AccessFeature PaperArticle

Adapted or Adaptable: How to Manage Entropy Production?

by Christophe Goupil and Eric Herbert

Entropy 2020, 22(1), 29; https://doi.org/10.3390/e22010029 - 24 Dec 2019

Cited by 7 | Viewed by 3694

Abstract

Adaptable or adapted? Whether it is a question of physical, biological, or even economic systems, this problem arises when all these systems are the location of matter and energy conversion. To this interdisciplinary question, we propose a theoretical framework based on the two principles of thermodynamics. Considering a finite time linear thermodynamic approach, we show that non-equilibrium systems operating in a quasi-static regime are quite deterministic as long as boundary conditions are correctly defined. The Novikov–Curzon–Ahlborn derivation applied to non-endoreversible systems then makes it possible to precisely determine the conditions for obtaining characteristic operating points. As a result, power maximization principle (MPP), entropy minimization principle (mEP), efficiency maximization, or waste minimization states are only specific modalities of system operation. We show that boundary conditions play a major role in defining operating points because they define the intensity of the feedback that ultimately characterizes the operation. Armed with these thermodynamic foundations, we show that the intrinsically most efficient systems are also the most constrained in terms of controlling the entropy and dissipation production. In particular, we show that the best figure of merit necessarily leads to a vanishing production of power. On the other hand, a class of systems emerges, which, although they do not offer extreme efficiency or power, have a wide range of use and therefore marked robustness. It therefore appears that the number of degrees of freedom of the system leads to an optimization of the allocation of entropy production. Full article

(This article belongs to the Special Issue Simulation with Entropy Thermodynamics)

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22 pages, 1265 KiB

Open AccessFeature PaperArticle

Variational Autoencoder Reconstruction of Complex Many-Body Physics

by Ilia A. Luchnikov, Alexander Ryzhov, Pieter-Jan Stas, Sergey N. Filippov and Henni Ouerdane

Entropy 2019, 21(11), 1091; https://doi.org/10.3390/e21111091 - 7 Nov 2019

Cited by 23 | Viewed by 6809

Abstract

Thermodynamics is a theory of principles that permits a basic description of the macroscopic properties of a rich variety of complex systems from traditional ones, such as crystalline solids, gases, liquids, and thermal machines, to more intricate systems such as living organisms and black holes to name a few. Physical quantities of interest, or equilibrium state variables, are linked together in equations of state to give information on the studied system, including phase transitions, as energy in the forms of work and heat, and/or matter are exchanged with its environment, thus generating entropy. A more accurate description requires different frameworks, namely, statistical mechanics and quantum physics to explore in depth the microscopic properties of physical systems and relate them to their macroscopic properties. These frameworks also allow to go beyond equilibrium situations. Given the notably increasing complexity of mathematical models to study realistic systems, and their coupling to their environment that constrains their dynamics, both analytical approaches and numerical methods that build on these models show limitations in scope or applicability. On the other hand, machine learning, i.e., data-driven, methods prove to be increasingly efficient for the study of complex quantum systems. Deep neural networks, in particular, have been successfully applied to many-body quantum dynamics simulations and to quantum matter phase characterization. In the present work, we show how to use a variational autoencoder (VAE)—a state-of-the-art tool in the field of deep learning for the simulation of probability distributions of complex systems. More precisely, we transform a quantum mechanical problem of many-body state reconstruction into a statistical problem, suitable for VAE, by using informationally complete positive operator-valued measure. We show, with the paradigmatic quantum Ising model in a transverse magnetic field, that the ground-state physics, such as, e.g., magnetization and other mean values of observables, of a whole class of quantum many-body systems can be reconstructed by using VAE learning of tomographic data for different parameters of the Hamiltonian, and even if the system undergoes a quantum phase transition. We also discuss challenges related to our approach as entropy calculations pose particular difficulties. Full article

(This article belongs to the Special Issue Simulation with Entropy Thermodynamics)

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27 pages, 454 KiB

Open AccessArticle

Non-Equilibrium Quantum Brain Dynamics: Super-Radiance and Equilibration in 2 + 1 Dimensions

by Akihiro Nishiyama, Shigenori Tanaka and Jack A. Tuszynski

Entropy 2019, 21(11), 1066; https://doi.org/10.3390/e21111066 - 30 Oct 2019

Cited by 7 | Viewed by 3447

Abstract

We derive time evolution equations, namely the Schrödinger-like equations and the Klein–Gordon equations for coherent fields and the Kadanoff–Baym (KB) equations for quantum fluctuations, in quantum electrodynamics (QED) with electric dipoles in

2 + 1

dimensions. Next we introduce a kinetic entropy current [...] Read more.

2 + 1

dimensions. Next we introduce a kinetic entropy current based on the KB equations in the first order of the gradient expansion. We show the H-theorem for the leading-order self-energy in the coupling expansion (the Hartree–Fock approximation). We show conserved energy in the spatially homogeneous systems in the time evolution. We derive aspects of the super-radiance and the equilibration in our single Lagrangian. Our analysis can be applied to quantum brain dynamics, that is QED, with water electric dipoles. The total energy consumption to maintain super-radiant states in microtubules seems to be within the energy consumption to maintain the ordered systems in a brain. Full article

(This article belongs to the Special Issue Simulation with Entropy Thermodynamics)

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16 pages, 7565 KiB

Open AccessArticle

Segmented Thermoelectric Generator under Variable Pulsed Heat Input Power

by Pablo Eduardo Ruiz-Ortega, Miguel Angel Olivares-Robles and Olao Yair Enciso-Montes de Oca

Entropy 2019, 21(10), 929; https://doi.org/10.3390/e21100929 - 24 Sep 2019

Cited by 6 | Viewed by 4010

Abstract

In this paper, we consider the transient state behavior of a segmented thermoelectric generator (STEG) exposed to a variable heat input power on the hot side while the transfer of heat on the cold side is by natural convection. Numerical analysis is used to calculate the power generation of the system. A one-dimensional STEG model, which includes Joule heating, the Peltier effect with constant properties of materials, is considered and governing equations are solved using the finite differences method. The transient analysis of this model is typical for energy harvesting applications. A novel design methodology, formulated on the ratio of the figure of merit of the thermoelectric materials, is developed including segmentation on the legs of the thermoelectric generator, which does not consider previous studies. In our approach, the figure of merit is an advantageous parameter to analyze its impact on thermal and electrical efficiency. The transient state of the thermoelectric generator is analyzed, considering two and three heat input sources. We obtain the temperature profiles, voltage generation, and efficiency of the STEG under pulsed heat input power. The results showed that the temperature drop along the semiconductor elements was more considerable when three pulses were applied, and when the thermal conductivity in the first segment was higher than that of the second segment. Furthermore, we show that the generated voltage and the maximum efficiency in the system occur when the value of the figure of merit in the first segment, which is in contact with the temperature source, is lower than the figure of merit for the second thermoelectric segment of the leg. The model investigated in this paper offers an essential guide on the thermal and electrical performance behavior of the system under transient conditions, which are present in many variable thermal phenomena such as solar radiation and the normalized driving cycles of an automotive thermoelectric generator. Full article

(This article belongs to the Special Issue Simulation with Entropy Thermodynamics)

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