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Entropy
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200 Years Anniversary of “Sadi Carnot, Réflexions Sur La Puissance...
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200 Years Anniversary of “Sadi Carnot, Réflexions Sur La Puissance Motrice Du Feu”; Bachelier: Paris, France, 1824

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

Deadline for manuscript submissions: closed (31 December 2024) | Viewed by 9048

Special Issue Editors

Prof. Dr. Armin Feldhoff

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Guest 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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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
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Pascal Boulet

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Guest Editor
Department of Chemistry, Aix-Marseille University, 13013 Marseille, France
Interests: thermoelectricity; bonding in materials; structure–properties relationships
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Prof. Dr. Marie-Christine Record

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Guest Editor
Faculty of Sciences, Aix Marseille Univ, CNRS, IM2NP, F-13013 Marseille, France
Interests: materials for energy; thermoelectrics; structure-properties relationships; density funstional theory calculations; quantum theory in atoms and molecules; phase stability; phase equilibria; chalcogenides
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Dr. Eric Herbert

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LIED laboratory, Université Paris Cité, 75013 Paris, France
Interests: power production in living systems, branching and growing network
Special Issues, Collections and Topics in MDPI journals
Dr. Gaël Giraud

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Guest Editor
Centre National de la Recherche Scientifique McCourt School of Public Policy, Georgetown University, Washington, DC 20057, USA
Interests: economic
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Dr. Mathieu Arnoux

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Guest Editor
École des Hautes Études en Sciences Sociales, Université Paris Cité, Paris, France
Interests: preindustrial technology and economics; non sustainable economical systems; energy technological systems

Special Issue Information

Dear Colleagues,

The 1824 book by Sadi Carnot was no less than the cradle of thermodynamics. It has influenced different disciplines, including physics, chemistry, biology, geology, engineering and materials science. Thermodynamics provides the framework for a generalized dynamics covering all kind of energy conversion in the living and non-living world, including metabolic pathways, chemical reactions, thermoelectricity and Hamiltonian mechanics. In harmonized appearance, all balance equations for extensive quantities (e.g. mass, momentum, angular momentum, entropy, electric charge, chemical substance, energy) follow the same format and reflect the uniformity in the basic principles. Thermodynamics covers both equilibrium and non-equilibrium systems. It is compatible with relativistic theory and field theories and, when complemented by statistical concepts, it comprises phenomena that traditionally fall in the domain of quantum mechanics. Thermodynamics is widely viewed as one of the sound standing and far-reaching concepts in science, technology, engineering and mathematics (STEM). 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 all branches of thermodynamics. Critical reflections on the historical development of the field of thermodynamics also fall within the scope of this Special Issue.

Prof. Dr. Armin Feldhoff
Prof. Dr. Christophe Goupil
Prof. Dr. Pascal Boulet
Prof. Dr. Marie-Christine Record
Dr. Eric Herbert
Dr. Gaël Giraud
Dr. Mathieu Arnoux
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.

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Published Papers (7 papers)

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Research

6 pages, 181 KiB  
Article
The Gibbs Fundamental Relation as a Tool for Relativity
by Friedrich Herrmann and Michael Pohlig
Entropy 2025, 27(1), 74; https://doi.org/10.3390/e27010074 - 15 Jan 2025
Abstract
When relativistic physics is lectured on, interest is focused on the behavior of mechanical and electromagnetic quantities during a reference frame change. However, not only mechanical and electromagnetic quantities transform during a reference frame change; thermodynamic and chemical quantities do too. We will [...] Read more.
When relativistic physics is lectured on, interest is focused on the behavior of mechanical and electromagnetic quantities during a reference frame change. However, not only mechanical and electromagnetic quantities transform during a reference frame change; thermodynamic and chemical quantities do too. We will study the transformations of temperature and chemical potential, show how to obtain the corresponding transformation equations with little effort, and exploit the fact that the energy conjugate extensive quantities, namely entropy and amount of substance, are Lorentz-invariant. Full article
(This article belongs to the Special Issue 200 Years Anniversary of “Sadi Carnot, Réflexions Sur La Puissance Motrice Du Feu”; Bachelier: Paris, France, 1824)
12 pages, 261 KiB  
Article
Fundamental Limits of an Irreversible Heat Engine
by Rui Fu
Entropy 2024, 26(12), 1128; https://doi.org/10.3390/e26121128 - 23 Dec 2024
Viewed by 395
Abstract
We investigated the optimal performance of an irreversible Stirling-like heat engine described by both overdamped and underdamped models within the framework of stochastic thermodynamics. By establishing a link between energy dissipation and Wasserstein distance, we derived the upper bound of maximal power that [...] Read more.
We investigated the optimal performance of an irreversible Stirling-like heat engine described by both overdamped and underdamped models within the framework of stochastic thermodynamics. By establishing a link between energy dissipation and Wasserstein distance, we derived the upper bound of maximal power that can be delivered over a complete engine cycle for both models. Additionally, we analytically developed an optimal control strategy to achieve this upper bound of maximal power and determined the efficiency at maximal power in the overdamped scenario. Full article
(This article belongs to the Special Issue 200 Years Anniversary of “Sadi Carnot, Réflexions Sur La Puissance Motrice Du Feu”; Bachelier: Paris, France, 1824)
32 pages, 5394 KiB  
Article
Carnot and the Archetype of Waterfalls
by Hans U. Fuchs, Elisabeth Dumont and Federico Corni
Entropy 2024, 26(12), 1066; https://doi.org/10.3390/e26121066 - 7 Dec 2024
Viewed by 606
Abstract
Carnot treats Heat as a Force of Nature, with its typical fundamental characteristics of intensity and thermal tension (temperature and temperature difference), extension (amount of heat, i.e., caloric), and power. To suggest how the three aspects are related, he applies the imagery of [...] Read more.
Carnot treats Heat as a Force of Nature, with its typical fundamental characteristics of intensity and thermal tension (temperature and temperature difference), extension (amount of heat, i.e., caloric), and power. To suggest how the three aspects are related, he applies the imagery of waterfalls to causative thermal processes: heat powers motion in a heat engine just as falling water does when activating rotation in a water wheel. We understand Carnot’s waterfall imagery as an archetype of human reasoning—as an embodiment of how we experience and understand causative (agentive) phenomena. We project it onto the macroscopic phenomena identified in physical science and so unlock the power of analogical structure mapping between theories of fluids, electricity and magnetism, heat, substances, gravity, and linear and rotational motion. In particular, the notion of (motive) power of a waterfall lets us create imaginative explanations of the interactions of Forces of Nature and helps us construct a generalized energy principle. Two-hundred years after Carnot made us aware of it, his Waterfall Analogy is a powerful example of theory construction with roots deep in how we experience phenomena as caused by natural agents. Full article
(This article belongs to the Special Issue 200 Years Anniversary of “Sadi Carnot, Réflexions Sur La Puissance Motrice Du Feu”; Bachelier: Paris, France, 1824)
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21 pages, 478 KiB  
Article
Exploring the Thermodynamic Uncertainty Constant: Insights from a Quasi-Ideal Nano-Gas Model
by Giorgio Sonnino
Entropy 2024, 26(12), 1011; https://doi.org/10.3390/e26121011 - 23 Nov 2024
Viewed by 447
Abstract
In previous work, we investigated thermodynamic processes in systems at the mesoscopic level where traditional thermodynamic descriptions (macroscopic or microscopic) may not be fully adequate. The key result is that entropy in such systems does not change continuously, as in macroscopic systems, but [...] Read more.
In previous work, we investigated thermodynamic processes in systems at the mesoscopic level where traditional thermodynamic descriptions (macroscopic or microscopic) may not be fully adequate. The key result is that entropy in such systems does not change continuously, as in macroscopic systems, but rather in discrete steps characterized by the quantization constant β. This quantization reflects the underlying discrete nature of the collision process in low-dimensional systems and the essential role played by thermodynamic fluctuations at this scale. Thermodynamic variables conjugate to the forces, along with Glansdorff–Prigogine’s dissipative variable can be discretized, enabling a mesoscopic-scale formulation of canonical commutation rules (CCRs). In this framework, measurements correspond to determining the eigenvalues of operators associated with key thermodynamic quantities. This work investigates the quantization parameter β in the CCRs using a nano-gas model analyzed through classical statistical physics. Our findings suggest that β is not an unknown fundamental constant. Instead, it emerges as the minimum achievable value derived from optimizing the uncertainty relation within the framework of our model. The expression for β is determined in terms of the ratio χ, which provides a dimensionless number that reflects the relative scales of volume and mass between entities at the Bohr (atomic level) and the molecular scales. This latter parameter quantifies the relative influence of quantum effects versus classical dynamics in a given scattering process. Full article
(This article belongs to the Special Issue 200 Years Anniversary of “Sadi Carnot, Réflexions Sur La Puissance Motrice Du Feu”; Bachelier: Paris, France, 1824)
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19 pages, 903 KiB  
Article
A Contemporary View on Carnot’s Réflexions
by Jan-Peter Meyn
Entropy 2024, 26(12), 1002; https://doi.org/10.3390/e26121002 - 21 Nov 2024
Viewed by 491
Abstract
Entropy and energy had not yet been introduced to physics by the time Carnot wrote his seminal Réflexions. Scholars continue to discuss what he really had in mind and what misconceptions he might have had. Actually, his work can be read as a [...] Read more.
Entropy and energy had not yet been introduced to physics by the time Carnot wrote his seminal Réflexions. Scholars continue to discuss what he really had in mind and what misconceptions he might have had. Actually, his work can be read as a correct introduction to the physics of heat engines when the term calorique is replaced by entropy and entropy is used as the other fundamental thermal quantity besides temperature. Carnot’s concepts of falling entropy as an analogy to the waterfall, and the separation of real thermal processes into reversible and irreversible processes are adopted. Some details of Carnot’s treatise are ignored, but the principal ideas are quoted and assumed without modification. With only two thermal quantities, temperature and entropy, modern heat engines can be explained in detail. Only after the principal function of heat engines is developed is energy introduced as physical quantity in order to compare thermal engines with mechanical and electrical engines and, specifically, to calculate efficiency. Full article
(This article belongs to the Special Issue 200 Years Anniversary of “Sadi Carnot, Réflexions Sur La Puissance Motrice Du Feu”; Bachelier: Paris, France, 1824)
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18 pages, 413 KiB  
Article
Phase Space Spin-Entropy
by Davi Geiger
Entropy 2024, 26(5), 372; https://doi.org/10.3390/e26050372 - 28 Apr 2024
Viewed by 2231
Abstract
Quantum physics is intrinsically probabilistic, where the Born rule yields the probabilities associated with a state that deterministically evolves. The entropy of a quantum state quantifies the amount of randomness (or information loss) of such a state. The degrees of freedom of a [...] Read more.
Quantum physics is intrinsically probabilistic, where the Born rule yields the probabilities associated with a state that deterministically evolves. The entropy of a quantum state quantifies the amount of randomness (or information loss) of such a state. The degrees of freedom of a quantum state are position and spin. We focus on the spin degree of freedom and elucidate the spin-entropy. Then, we present some of its properties and show how entanglement increases spin-entropy. A dynamic model for the time evolution of spin-entropy concludes the paper. Full article
(This article belongs to the Special Issue 200 Years Anniversary of “Sadi Carnot, Réflexions Sur La Puissance Motrice Du Feu”; Bachelier: Paris, France, 1824)
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21 pages, 392 KiB  
Article
Testing the Minimum System Entropy and the Quantum of Entropy
by Uwe Hohm and Christoph Schiller
Entropy 2023, 25(11), 1511; https://doi.org/10.3390/e25111511 - 3 Nov 2023
Cited by 1 | Viewed by 2835
Abstract
Experimental and theoretical results about entropy limits for macroscopic and single-particle systems are reviewed. All experiments confirm the minimum system entropy S⩾kln2. We clarify in which cases it is possible to speak about a minimum system entropy [...] Read more.
Experimental and theoretical results about entropy limits for macroscopic and single-particle systems are reviewed. All experiments confirm the minimum system entropy S⩾kln2. We clarify in which cases it is possible to speak about a minimum system entropykln2 and in which cases about a quantum of entropy. Conceptual tensions with the third law of thermodynamics, with the additivity of entropy, with statistical calculations, and with entropy production are resolved. Black hole entropy is surveyed. Claims for smaller system entropy values are shown to contradict the requirement of observability, which, as possibly argued for the first time here, also implies the minimum system entropy kln2. The uncertainty relations involving the Boltzmann constant and the possibility of deriving thermodynamics from the existence of minimum system entropy enable one to speak about a general principle that is valid across nature. Full article
(This article belongs to the Special Issue 200 Years Anniversary of “Sadi Carnot, Réflexions Sur La Puissance Motrice Du Feu”; Bachelier: Paris, France, 1824)
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