Special Issue "Simulation with Entropy Thermodynamics"

A special issue of Entropy (ISSN 1099-4300).

Deadline for manuscript submissions: 31 December 2019.

Special Issue Editor

Prof. Dr. Christophe Goupil
E-Mail Website
Guest Editor
Universite Paris 7- Denis Diderot, Paris, France
Interests: out-of-equilibrium thermodynamics; solid-state physics; thermoelectricity; living systems; thermodynamics optimization; network thermodynamics; ecological economics

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

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 papers will be 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 1600 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.

Keywords

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

Published Papers (3 papers)

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Research

Open AccessFeature PaperArticle
Variational Autoencoder Reconstruction of Complex Many-Body Physics
Entropy 2019, 21(11), 1091; https://doi.org/10.3390/e21111091 - 07 Nov 2019
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 [...] Read more.
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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Open AccessArticle
Non-Equilibrium Quantum Brain Dynamics: Super-Radiance and Equilibration in 2 + 1 Dimensions
Entropy 2019, 21(11), 1066; https://doi.org/10.3390/e21111066 - 30 Oct 2019
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.
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 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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Open AccessArticle
Segmented Thermoelectric Generator under Variable Pulsed Heat Input Power
Entropy 2019, 21(10), 929; https://doi.org/10.3390/e21100929 - 24 Sep 2019
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 [...] Read more.
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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Planned Papers

The below list represents only planned manuscripts. Some of these manuscripts have not been received by the Editorial Office yet. Papers submitted to MDPI journals are subject to peer-review.

Title: Thermodynamic Properties of Equilibrium Debye Plasmas
Authors: Annarita Laricchiuta and Gianpiero Colonna
Affiliation: Istituto per la Scienza e Tecnologia dei Plasmi ISTP CNR, Bari Section (Italy)
Abstract: The thermodynamic 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 treatment of these plasmas requires in principle the reformulation of the statistical mechanics in terms of a global Hamiltonian for the whole gas, instead of the usual separable form of non-interacting chemical species characterized through internal and translational partition functions. The complexity of the rigorous approach led to the development of simplified models, able to include the neighbor-effects on the isolated system though remaining consistent with the traditional thermodynamic approach. High-density conditions have been simulated assuming particle interactions described by a screened Coulomb potential.

Title: Adaptable or Adapted? A Question of Entropy Allocation
Authors: Christophe Goupil and Eric Herbert
Affiliation: University of Paris, LIED, CNRS UMR 8236, Paris, France
Abstract: Adaptable or adapted? This ancient question is equally relevant in biology, economics, history of technologies and, of course, physics. In various forms, it is now being reformulated with a particular acuity, which is the one posed by the ecological transition. When it comes to lasting, to going through this transition, the question arises as to which solution to choose? The one with the highest efficiency, both in terms of efficiency and power? Or the one that offers the greatest resilience and focuses on endurance? To this interdisciplinary question we propose a theoretical framework based on the two principles of thermodynamics.  Considering a finite time thermodynamic approach, we show that out-of-equilibrium systems operating in quasi-static regime are quite deterministic as long as boundary conditions are correctly defined. The Novikov-Curzon-Ahlborn approach applied to non-endoreversible systems makes it possible to precisely locate the conditions for obtaining characteristic operating points. As a result, power maximization (MPP), entropy minimization (mEP), efficiency maximization, or waste minimization states are only specific modalities of system operation. The question of boundary conditions is then central because it determines the presence and intensity of the feedbacks that ultimately characterize the operating point. With these thermodynamic and feedback foundations in mind, we show that the most efficient systems are also the most constrained in terms of negative externalities and range of use. Among the less efficient systems, there is a class of systems that, although they do not offer extreme efficiency and power, have a wide operating range and high resilience. The determination of these systems is based both on the level of entropy production considered acceptable, on the one hand, and on the allocation of this production to the various sources of production of the latter. It therefore appears that the number of degrees of freedom of the system leads to an optimization of entropy production. Beyond the traditional functionalities of force-flow products according to Onsager, a practical simulation framework is proposed, which makes it possible to consider purely physical configurations, as well as biological or economic configurations.

Title: Variational Autoencoder Reconstruction of Complex Many-Body Quantum System Physics
Authors: Ilya Luchnikov 1,2, Alexander Ryzhov 1, Pieter-Jan Stas 3, Sergey N. Filippov 2,4,5 and Henni Ouerdane 1
Affiliations:
1. Center for Energy Science and Technology, Skolkovo Institute of Science and Technology, 3 Nobel Street, Skolkovo, Moscow Region 121205, Russia
2. Moscow Institute of Physics and Technology, Institutskii Per. 9, Dolgoprudny, Moscow Region 141700, Russia
3. Department of Applied Physics and Ginzton Laboratory, Stanford University 348 Via Pueblo Mall, Stanford, California 94305, USA
4. Valiev Institute of Physics and Technology of Russian, Academy of Sciences, Nakhimovskii Pr. 34, Moscow 117218, Russia
5. Steklov Mathematical Institute of Russian Academy of Sciences, Gubkina St. 8, Moscow 119991, Russia
Abstract: Machine learning 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 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 into a statistical problem, suitable for VAE, by using informationally complete positive operator-valued measure. We show with the illustrative case of the 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.

Title: Non-equilibrium Quantum Brain Dynamics: Super-radiance and Equilibration in 2 + 1 Dimensions
Authors:Akihiro Nishiyama 1, Shigenori Tanaka 1 and Jack A. Tuszynski 2,3
Affiliations:
1 Graduate School of System Informatics, Kobe University, 1-1 Rokkodai, Nada-ku, Kobe, 657-8501, Japan
2 Department of Oncology, University of Alberta, Cross Cancer Institute, Edmonton, Alberta, Canada T6G 1Z2
3 Department of Physics, University of Alberta, Edmonton, Alberta, Canada T6G 2J1
Abstract: We derive time evolution equations, namely the Schrodinger-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 based on the KB equations in the 1st 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 a 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.

 

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