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Nature of Entropy and Its Direct Metrology

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

Deadline for manuscript submissions: closed (31 August 2022) | Viewed by 27005

Special Issue Editor

Institute of Physical Chemistry and Electrochemistry, Leibniz University Hannover, Callinstr. 3A, 30167 Hannover, Germany
Interests: thermo-iono-electronic materials; oxygen transport membranes; hydrogen transport membranes; triple conductors; nature of entropy; metrology of entropy; nonequilibrium thermodynamics; thermodynamics of small systems; thermoelectricity; thermocells; thermodiffusion; energy harvesting
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Special Issue Information

Dear Colleagues,

Thermodynamics has identified entropy as the central operational quantity in any kind of heat engine. Entropy can fall down its thermodynamic potential, which is the absolute temperature, and released energy is transferred towards a useful process. For instance, entropy drives thermoelectric generators and thermogalvanic cells to generate electrical power, as well as Stirling motors to generate mechanical power. In reversed operation, these devices can be used as entropy pumps and transport entropy from a low temperature to a high temperature. Entropy pumps are used in domestic heating, air conditioning, and refrigeration. To achieve a high conversion efficiency, it is crucial to maintain a low dissipation of entropy and of thermal energy by minimizing entropy production. The central role of entropy in thermal processes demands a better understanding of its nature and of the entropic properties of gases, liquids, and solids in terms of entropy capacity, entropy capacitance, entropy current, entropy current density, entropy conductivity, and entropy conductance. The metrology of these entropic quantities requires reflections on adequate units of measurement, as well as the realization of measurements in practice and their traceability. Contributions addressing any of these issues are very welcome.

This Special Issue aims to be a forum for the presentation of new and improved insight into the nature of entropy and its metrology. Instructive analyses of the thermal processes and critical reflections on the historical perception of entropy in the field of thermodynamics fall within the scope of this Special Issue.

 Prof. Dr. Armin Feldhoff

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 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.

Keywords

  • entropy
  • thermodynamic potential
  • thermal energy
  • entropy capacity
  • entropy current
  • entropy conductivity
  • entropy conductance
  • heat engine
  • entropy pump
  • metrology

Published Papers (9 papers)

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Research

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22 pages, 560 KiB  
Article
On Quantum Entropy
by Davi Geiger and Zvi M. Kedem
Entropy 2022, 24(10), 1341; https://doi.org/10.3390/e24101341 - 23 Sep 2022
Cited by 3 | Viewed by 4157
Abstract
Quantum physics, despite its intrinsically probabilistic nature, lacks a definition of entropy fully accounting for the randomness of a quantum state. For example, von Neumann entropy quantifies only the incomplete specification of a quantum state and does not quantify the probabilistic distribution of [...] Read more.
Quantum physics, despite its intrinsically probabilistic nature, lacks a definition of entropy fully accounting for the randomness of a quantum state. For example, von Neumann entropy quantifies only the incomplete specification of a quantum state and does not quantify the probabilistic distribution of its observables; it trivially vanishes for pure quantum states. We propose a quantum entropy that quantifies the randomness of a pure quantum state via a conjugate pair of observables/operators forming the quantum phase space. The entropy is dimensionless, it is a relativistic scalar, it is invariant under canonical transformations and under CPT transformations, and its minimum has been established by the entropic uncertainty principle. We expand the entropy to also include mixed states. We show that the entropy is monotonically increasing during a time evolution of coherent states under a Dirac Hamiltonian. However, in a mathematical scenario, when two fermions come closer to each other, each evolving as a coherent state, the total system’s entropy oscillates due to the increasing spatial entanglement. We hypothesize an entropy law governing physical systems whereby the entropy of a closed system never decreases, implying a time arrow for particle physics. We then explore the possibility that as the oscillations of the entropy must by the law be barred in quantum physics, potential entropy oscillations trigger annihilation and creation of particles. Full article
(This article belongs to the Special Issue Nature of Entropy and Its Direct Metrology)
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18 pages, 634 KiB  
Article
Spin Entropy
by Davi Geiger and Zvi M. Kedem
Entropy 2022, 24(9), 1292; https://doi.org/10.3390/e24091292 - 14 Sep 2022
Cited by 4 | Viewed by 2222
Abstract
Two types of randomness are associated with a mixed quantum state: the uncertainty in the probability coefficients of the constituent pure states and the uncertainty in the value of each observable captured by the Born’s rule probabilities. Entropy is a quantification of randomness, [...] Read more.
Two types of randomness are associated with a mixed quantum state: the uncertainty in the probability coefficients of the constituent pure states and the uncertainty in the value of each observable captured by the Born’s rule probabilities. Entropy is a quantification of randomness, and we propose a spin-entropy for the observables of spin pure states based on the phase space of a spin as described by the geometric quantization method, and we also expand it to mixed quantum states. This proposed entropy overcomes the limitations of previously-proposed entropies such as von Neumann entropy which only quantifies the randomness of specifying the quantum state. As an example of a limitation, previously-proposed entropies are higher for Bell entangled spin states than for disentangled spin states, even though the spin observables are less constrained for a disentangled pair of spins than for an entangled pair. The proposed spin-entropy accurately quantifies the randomness of a quantum state, it never reaches zero value, and it is lower for entangled states than for disentangled states. Full article
(This article belongs to the Special Issue Nature of Entropy and Its Direct Metrology)
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44 pages, 2198 KiB  
Article
Entropy and the Experience of Heat
by Hans U. Fuchs, Michele D’Anna and Federico Corni
Entropy 2022, 24(5), 646; https://doi.org/10.3390/e24050646 - 04 May 2022
Cited by 5 | Viewed by 2013
Abstract
We discuss how to construct a direct and experientially natural path to entropy as a extensive quantity of a macroscopic theory of thermal systems and processes. The scientific aspects of this approach are based upon continuum thermodynamics. We ask what the roots of [...] Read more.
We discuss how to construct a direct and experientially natural path to entropy as a extensive quantity of a macroscopic theory of thermal systems and processes. The scientific aspects of this approach are based upon continuum thermodynamics. We ask what the roots of an experientially natural approach might be—to this end we investigate and describe in some detail (a) how humans experience and conceptualize an extensive thermal quantity (i.e., an amount of heat), and (b) how this concept evolved during the early development of the science of thermal phenomena (beginning with the Experimenters of the Accademia del Cimento and ending with Sadi Carnot). We show that a direct approach to entropy, as the extensive quantity of models of thermal systems and processes, is possible and how it can be applied to the teaching of thermodynamics for various audiences. Full article
(This article belongs to the Special Issue Nature of Entropy and Its Direct Metrology)
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12 pages, 894 KiB  
Article
A Robust Protocol for Entropy Measurement in Mesoscopic Circuits
by Timothy Child, Owen Sheekey, Silvia Lüscher, Saeed Fallahi, Geoffrey C. Gardner, Michael Manfra and Joshua Folk
Entropy 2022, 24(3), 417; https://doi.org/10.3390/e24030417 - 17 Mar 2022
Cited by 12 | Viewed by 2788
Abstract
Previous measurements utilizing Maxwell relations to measure change in entropy, S, demonstrated remarkable accuracy in measuring the spin-1/2 entropy of electrons in a weakly coupled quantum dot. However, these previous measurements relied upon prior knowledge of the charge transition lineshape. This had [...] Read more.
Previous measurements utilizing Maxwell relations to measure change in entropy, S, demonstrated remarkable accuracy in measuring the spin-1/2 entropy of electrons in a weakly coupled quantum dot. However, these previous measurements relied upon prior knowledge of the charge transition lineshape. This had the benefit of making the quantitative determination of entropy independent of scale factors in the measurement itself but at the cost of limiting the applicability of the approach to simple systems. To measure the entropy of more exotic mesoscopic systems, a more flexible analysis technique may be employed; however, doing so requires a precise calibration of the measurement. Here, we give details on the necessary improvements made to the original experimental approach and highlight some of the common challenges (along with strategies to overcome them) that other groups may face when attempting this type of measurement. Full article
(This article belongs to the Special Issue Nature of Entropy and Its Direct Metrology)
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27 pages, 883 KiB  
Article
Coupled Transport Effects in Solid Oxide Fuel Cell Modeling
by Aydan Gedik, Nico Lubos and Stephan Kabelac
Entropy 2022, 24(2), 224; https://doi.org/10.3390/e24020224 - 31 Jan 2022
Cited by 5 | Viewed by 2741
Abstract
With its outstanding performance characteristics, the SOFC represents a promising technology for integration into the current energy supply system. For cell development and optimization, a reliable quantitative description of the transport mechanisms and the resulting losses are relevant. The local transport processes are [...] Read more.
With its outstanding performance characteristics, the SOFC represents a promising technology for integration into the current energy supply system. For cell development and optimization, a reliable quantitative description of the transport mechanisms and the resulting losses are relevant. The local transport processes are calculated by a 1D model based on the non-equilibrium thermodynamics (NET). The focus of this study is the mass transport in the gas diffusion layers (GDL), which was described as simplified by Fick’s law in a previously developed model. This is first replaced by the Dusty-Gas model (DGM) and then by the thermal diffusion (Soret effect) approach. The validation of the model was performed by measuring U,j-characteristics resulting in a maximum deviation of experimental to simulated cell voltage to up to 0.93%. It is shown that, under the prevailing temperature, gradients the Soret effect can be neglected, but the extension to the DGM has to be considered. The temperature and heat flow curves illustrate the relevance of the Peltier effects. At T=1123.15 K and j=8000 A/m2, 64.44% of the total losses occur in the electrolyte. The exergetic efficiency for this operating point is 0.42. Since lower entropy production rates can be assumed in the GDL, the primary need is to investigate alternative electrolyte materials. Full article
(This article belongs to the Special Issue Nature of Entropy and Its Direct Metrology)
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17 pages, 763 KiB  
Article
Which Physical Quantity Deserves the Name “Quantity of Heat”?
by Friedrich Herrmann and Michael Pohlig
Entropy 2021, 23(8), 1078; https://doi.org/10.3390/e23081078 - 19 Aug 2021
Cited by 8 | Viewed by 2878
Abstract
“What is heat?” was the title of a 1954 article by Freeman J. Dyson, published in Scientific American. Apparently, it was appropriate to ask this question at that time. The answer is given in the very first sentence of the article: heat is [...] Read more.
“What is heat?” was the title of a 1954 article by Freeman J. Dyson, published in Scientific American. Apparently, it was appropriate to ask this question at that time. The answer is given in the very first sentence of the article: heat is disordered energy. We will ask the same question again, but with a different expectation for its answer. Let us imagine that all the thermodynamic knowledge is already available: both the theory of phenomenological thermodynamics and that of statistical thermodynamics, including quantum statistics, but that the term “heat” has not yet been attributed to any of the variables of the theory. With the question “What is heat?” we now mean: which of the physical quantities deserves this name? There are several candidates: the quantities Q, H, Etherm and S. We can then formulate a desideratum, or a profile: What properties should such a measure of the quantity or amount of heat ideally have? Then, we evaluate all the candidates for their suitability. It turns out that the winner is the quantity S, which we know by the name of entropy. In the second part of the paper, we examine why entropy has not succeeded in establishing itself as a measure for the amount of heat, and we show that there is a real chance today to make up for what was missed. Full article
(This article belongs to the Special Issue Nature of Entropy and Its Direct Metrology)
14 pages, 2907 KiB  
Article
A Thermodynamic Approach to Measuring Entropy in a Few-Electron Nanodevice
by Eugenia Pyurbeeva and Jan A. Mol
Entropy 2021, 23(6), 640; https://doi.org/10.3390/e23060640 - 21 May 2021
Cited by 11 | Viewed by 3018
Abstract
The entropy of a system gives a powerful insight into its microscopic degrees of freedom; however, standard experimental ways of measuring entropy through heat capacity are hard to apply to nanoscale systems, as they require the measurement of increasingly small amounts of heat. [...] Read more.
The entropy of a system gives a powerful insight into its microscopic degrees of freedom; however, standard experimental ways of measuring entropy through heat capacity are hard to apply to nanoscale systems, as they require the measurement of increasingly small amounts of heat. Two alternative entropy measurement methods have been recently proposed for nanodevices: through charge balance measurements and transport properties. We describe a self-consistent thermodynamic framework for applying thermodynamic relations to few-electron nanodevices—small systems, where fluctuations in particle number are significant, whilst highlighting several ongoing misconceptions. We derive a relation (a consequence of a Maxwell relation for small systems), which describes both existing entropy measurement methods as special cases, while also allowing the experimentalist to probe the intermediate regime between them. Finally, we independently prove the applicability of our framework in systems with complex microscopic dynamics—those with many excited states of various degeneracies—from microscopic considerations. Full article
(This article belongs to the Special Issue Nature of Entropy and Its Direct Metrology)
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Review

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21 pages, 2646 KiB  
Review
On the Thermal Capacity of Solids
by Armin Feldhoff
Entropy 2022, 24(4), 479; https://doi.org/10.3390/e24040479 - 29 Mar 2022
Cited by 4 | Viewed by 2750
Abstract
The term thermal capacity appears to suggest a storable thermal quantity. However, this claim is not redeemed when thermal capacity is projected onto “heat”, which, like all energy forms, exits only in transit and is not a part of internal energy. The storable [...] Read more.
The term thermal capacity appears to suggest a storable thermal quantity. However, this claim is not redeemed when thermal capacity is projected onto “heat”, which, like all energy forms, exits only in transit and is not a part of internal energy. The storable thermal quantity is entropy, and entropy capacity is a well-defined physical coefficient which has the advantage of being a susceptibility. The inverse of the entropy capacity relates the response of the system (change of temperature) to a stimulus (change of entropy) such as the fluid level responses to a change in amount of fluid contained in a vessel. Frequently, entropy capacity has been used implicitly, which is clarified in examples of the low-temperature analysis of phononic and electronic contributions to the thermal capacity of solids. Generally, entropy capacity is used in the estimation of the entropy of a solid. Implicitly, the thermoelectric figure of merit refers to entropy capacity. The advantage of the explicit use of entropy capacity comes with a descriptive fundamental understanding of the thermal behaviour of solids, which is made clear by the examples of the Debye model of phonons in solids, the latest thermochemical modelling of carbon allotropes (diamond and graphite) and not least caloric materials. An electrocaloric cycle of barium titanate close to its paraelectric–ferroelectric phase transition is analysed by means of entropy capacity. Entropy capacity is a key to intuitively understanding thermal processes. Full article
(This article belongs to the Special Issue Nature of Entropy and Its Direct Metrology)
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32 pages, 1035 KiB  
Review
Quantum Transport of Particles and Entropy
by Christoph Strunk
Entropy 2021, 23(12), 1573; https://doi.org/10.3390/e23121573 - 25 Nov 2021
Cited by 5 | Viewed by 2295
Abstract
A unified view on macroscopic thermodynamics and quantum transport is presented. Thermodynamic processes with an exchange of energy between two systems necessarily involve the flow of other balancable quantities. These flows are first analyzed using a simple drift-diffusion model, which includes the thermoelectric [...] Read more.
A unified view on macroscopic thermodynamics and quantum transport is presented. Thermodynamic processes with an exchange of energy between two systems necessarily involve the flow of other balancable quantities. These flows are first analyzed using a simple drift-diffusion model, which includes the thermoelectric effects, and connects the various transport coefficients to certain thermodynamic susceptibilities and a diffusion coefficient. In the second part of the paper, the connection between macroscopic thermodynamics and quantum statistics is discussed. It is proposed to employ not particles, but elementary Fermi- or Bose-systems as the elementary building blocks of ideal quantum gases. In this way, the transport not only of particles but also of entropy can be derived in a concise way, and is illustrated both for ballistic quantum wires, and for diffusive conductors. In particular, the quantum interference of entropy flow is in close correspondence to that of electric current. Full article
(This article belongs to the Special Issue Nature of Entropy and Its Direct Metrology)
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