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Entropy
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Trends in the Second Law of Thermodynamics
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Trends in the Second Law of Thermodynamics

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

Deadline for manuscript submissions: 15 June 2025 | Viewed by 12346

Special Issue Editors

Prof. Dr. Roberto Zivieri

E-Mail Website1 Website2
Guest Editor
1. Department of Mathematical and Computer Sciences, Physical Sciences and Earth Sciences, University of Messina, 1, 98122 Messina, Italy
2. Istituto Nazionale di Alta Matematica (INdAM), 00185 Rome, Italy
Interests: solid state physics and lattice phonons dynamics; spin waves; ferromagnetic materials and nanostructures; low-dimensional magnetic systems; quantum magnetic models; magnonic crystals; magnetic metamaterials; magnetic signature of ships; quantum magnetic sensors; topological defects; magnetic vortices and antivortices; magnetic skyrmions; spin-transfer torque effect; spin-Hall effect; band structure and mobility calculation of topological semimetals and magnetoresistance; linear and nonlinear seismic metamaterials; statistical thermodynamics of biological systems; entropy of irreversible reactions in living systems; electrical power signals; distribution lines; smart grids
Special Issues, Collections and Topics in MDPI journals
Dr. Israa Medlej

E-Mail Website
Guest Editor
Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
Interests: quantum physics; spintronics; magnonics; microwave magnetics; topological spin textures; neuromorphic computing; nanophotonics; quantum optics; plasmonics; nanofabrication; integrated photonics and quantum technologies; micromagnetic simulations; theoretical calculations; experiments
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The Second Law of Thermodynamics is a fundamental law of the universe, and its ubiquity can be proven by demonstrating its equivalence across all types of thermodynamic systems. This law dictates the direction of energy transfer, which is always from a higher to a lower potential and is always irreversible. It sets the conditions for transferring mass and energy and, thus, the limitations of such processes. This simplicity of causation drives the inexorable movement of energy toward an equilibrium.

The need to delve further into the Second Law of Thermodynamics is essential. This Special Issue intends to assess certain physical and philosophical concepts, to spark dialogue and thoughtful criticism, including certain recent debates, as well as to gain a deeper understanding of the fundamental principles of the Second Law of Thermodynamics.

The Second Law of Thermodynamics is a significant and unassailable rule in physics, engineering, and, more generally, the natural world. It has been known for over 150 years and is usually considered the most authoritative law.

Earlier, Einstein firmly stated that “Thermodynamics is the only universal physical theory that will never be refuted”. The Second Law and other thermodynamics principles are connected to many perplexing matters that require delicate descriptions and fuzzy interpretations. 

We invite contributions to discuss the fundamental aspects of the Second Law of Thermodynamics, including entropy as a significant physical quantity characterizing a thermodynamic system and entropy generation as an indicator of irreversibility in a thermodynamic process.

We welcome all sorts of relevant topics, such as (but not limited to):

  • Entropy and the Second Law;
  • Clausius equality and inequality;
  • The reversibility and irreversibility of thermodynamic processes;
  • Statistical thermodynamics;
  • The Second Law of Thermodynamics within a classical and quantum description;
  • Low-temperature studies and experiments within the Second Law of Thermodynamics;
  • Bose–Einstein condensation and the Second Law of Thermodynamics;
  • Quantum coherence, entanglement, and the Second Law;
  • Maxwell’s demon and further challenges;
  • The Second Law in Cosmology, Gravitation, and Astrophysics.

It is our desire that this Special Issue motivates researchers and specialists to take a closer look at the Second Law of Thermodynamics—one of the most influential fundamental laws of nature—and the issues relevant to it.

Prof. Dr. Roberto Zivieri
Dr. Israa Medlej
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.

Keywords

  • Second Law of Thermodynamics in physics, chemistry, biology, engineering and natural science
  • entropy
  • Clausius equality
  • Clausius inequality
  • reversibility
  • irreversibility
  • non-equilibrium
  • Second Law in quantum theory
  • statistical thermodynamics
  • Maxwell’s demon

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Published Papers (7 papers)

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Editorial

Jump to: Research

6 pages, 253 KiB  
Editorial
Trends in the Second Law of Thermodynamics
by Roberto Zivieri
Entropy 2023, 25(9), 1321; https://doi.org/10.3390/e25091321 - 10 Sep 2023
Cited by 3 | Viewed by 3391
Abstract
The Second Law of Thermodynamics represents a milestone in the history of not only physics but also chemistry, engineering, and, more generally, life and natural sciences [...] Full article
(This article belongs to the Special Issue Trends in the Second Law of Thermodynamics)

Research

Jump to: Editorial

45 pages, 447 KiB  
Article
Revisions of the Phenomenological and Statistical Statements of the Second Law of Thermodynamics
by Grzegorz Marcin Koczan and Roberto Zivieri
Entropy 2024, 26(12), 1122; https://doi.org/10.3390/e26121122 - 22 Dec 2024
Viewed by 175
Abstract
The status of the Second Law of Thermodynamics, even in the 21st century, is not as certain as when Arthur Eddington wrote about it a hundred years ago. It is not only about the truth of this law, but rather about its strict [...] Read more.
The status of the Second Law of Thermodynamics, even in the 21st century, is not as certain as when Arthur Eddington wrote about it a hundred years ago. It is not only about the truth of this law, but rather about its strict and exhaustive formulation. In the previous article, it was shown that two of the three most famous thermodynamic formulations of the Second Law of Thermodynamics are non-exhaustive. However, the status of the statistical approach, contrary to common and unfounded opinions, is even more difficult. It is known that Boltzmann did not manage to completely and correctly derive the Second Law of Thermodynamics from statistical mechanics, even though he probably did everything he could in this regard. In particular, he introduced molecular chaos into the extension of the Liouville equation, obtaining the Boltzmann equation. By using the H theorem, Boltzmann transferred the Second Law of Thermodynamics thesis to the molecular chaos hypothesis, which is not considered to be fully true. Therefore, the authors present a detailed and critical review of the issue of the Second Law of Thermodynamics and entropy from the perspective of phenomenological thermodynamics and statistical mechanics, as well as kinetic theory. On this basis, Propositions 1–3 for the statements of the Second Law of Thermodynamics are formulated in the original part of the article. Proposition 1 is based on resolving the misunderstanding of the Perpetuum Mobile of the Second Kind by introducing the Perpetuum Mobile of the Third Kind. Proposition 2 specifies the structure of allowed thermodynamic processes by using the Inequality of Heat and Temperature Proportions inspired by Eudoxus of Cnidus’s inequalities defining real numbers. Proposition 3 is a Probabilistic Scheme of the Second Law of Thermodynamics that, like a game, shows the statistical tendency for entropy to increase, even though the possibility of it decreasing cannot be completely ruled out. Proposition 3 is, in some sense, free from Loschmidt’s irreversibility paradox. Full article
(This article belongs to the Special Issue Trends in the Second Law of Thermodynamics)
17 pages, 1607 KiB  
Article
Assessment of Nuclear Fusion Reaction Spontaneity via Engineering Thermodynamics
by Silvano Tosti
Entropy 2024, 26(10), 884; https://doi.org/10.3390/e26100884 - 21 Oct 2024
Viewed by 600
Abstract
This work recalls the basic thermodynamics of chemical processes for introducing the evaluation of the nuclear reactions’ spontaneity. The application and definition of the thermodynamic state functions of the nuclear processes have been described by focusing on their contribution to the chemical potential. [...] Read more.
This work recalls the basic thermodynamics of chemical processes for introducing the evaluation of the nuclear reactions’ spontaneity. The application and definition of the thermodynamic state functions of the nuclear processes have been described by focusing on their contribution to the chemical potential. The variation of the nuclear binding potentials involved in a nuclear reaction affects the chemical potential through a modification of the internal energy and of the other state functions. These energy changes are related to the mass defect between reactants and products of the nuclear reaction and are of the order of magnitude of 1 MeV per particle, about six orders of magnitude larger than those of the chemical reactions. In particular, this work assesses the Gibbs free energy change of the fusion reactions by assuming the Qvalue as the nuclear contribution to the chemical potential and by calculating the entropy through the Sackur–Tetrode expression. Then, the role of the entropy in fusion processes was re-examined by demonstrating the previous spontaneity analyses, which assume a perfect gas of DT atoms in the initial state of the fusion reactions, are conservative and lead to assessing more negative ΔG than in the real case (ionized gas). As a final point, this paper examines the thermodynamic spontaneity of exothermic processes with a negative change of entropy and discusses the different thermodynamic spontaneity exhibited by the DT fusion processes when conducted in a controlled or uncontrolled way. Full article
(This article belongs to the Special Issue Trends in the Second Law of Thermodynamics)
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11 pages, 1561 KiB  
Article
A Symmetric Form of the Clausius Statement of the Second Law of Thermodynamics
by Ti-Wei Xue, Tian Zhao and Zeng-Yuan Guo
Entropy 2024, 26(6), 514; https://doi.org/10.3390/e26060514 - 14 Jun 2024
Cited by 5 | Viewed by 1144
Abstract
Bridgman once reflected on thermodynamics that the laws of thermodynamics were formulated in their present form by the great founders of thermodynamics, Kelvin and Clausius, before all the essential physical facts were in, and there has been no adequate reexamination of the fundamentals [...] Read more.
Bridgman once reflected on thermodynamics that the laws of thermodynamics were formulated in their present form by the great founders of thermodynamics, Kelvin and Clausius, before all the essential physical facts were in, and there has been no adequate reexamination of the fundamentals since. Thermodynamics still has unknown possibilities waiting to be explored. This paper begins with a brief review of Clausius’s work on the second law of thermodynamics and a reassessment of the content of Clausius’s statement. The review tells that what Clausius originally referred to as the second law of thermodynamics was, in fact, the theorem of equivalence of transformations (TET) in a reversible cycle. On this basis, a new symmetric form of Clausius’s TET is proposed. This theorem says that the two transformations, i.e., the transformation of heat to work and the transformation of work from high pressure to low pressure, should be equivalent in a reversible work-to-heat cycle. New thermodynamic cyclic laws are developed on the basis of the cycle with two work reservoirs (two pressures), which enriches the fundamental of the second law of thermodynamics. Full article
(This article belongs to the Special Issue Trends in the Second Law of Thermodynamics)
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22 pages, 13068 KiB  
Article
Systems and Methods for Transformation and Degradation Analysis
by Jude A. Osara and Michael D. Bryant
Entropy 2024, 26(6), 454; https://doi.org/10.3390/e26060454 - 27 May 2024
Viewed by 1324
Abstract
Modern concepts in irreversible thermodynamics are applied to system transformation and degradation analyses. Phenomenological entropy generation (PEG) theorem is combined with the Degradation-Entropy Generation (DEG) theorem for instantaneous multi-disciplinary, multi-scale, multi-component system characterization. A transformation-PEG theorem and space materialize with system and process [...] Read more.
Modern concepts in irreversible thermodynamics are applied to system transformation and degradation analyses. Phenomenological entropy generation (PEG) theorem is combined with the Degradation-Entropy Generation (DEG) theorem for instantaneous multi-disciplinary, multi-scale, multi-component system characterization. A transformation-PEG theorem and space materialize with system and process defining elements and dimensions. The near-100% accurate, consistent results and features in recent publications demonstrating and applying the new TPEG methods to frictional wear, grease aging, electrochemical power system cycling—including lithium-ion battery thermal runaway—metal fatigue loading and pump flow are collated herein, demonstrating the practicality of the new and universal PEG theorem and the predictive power of models that combine and utilize both theorems. The methodology is useful for design, analysis, prognostics, diagnostics, maintenance and optimization. Full article
(This article belongs to the Special Issue Trends in the Second Law of Thermodynamics)
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12 pages, 319 KiB  
Article
Magnetic Black Hole Thermodynamics in an Extended Phase Space with Nonlinear Electrodynamics
by Sergey Il’ich Kruglov
Entropy 2024, 26(3), 261; https://doi.org/10.3390/e26030261 - 14 Mar 2024
Cited by 1 | Viewed by 1222
Abstract
We study Einstein’s gravity coupled to nonlinear electrodynamics with two parameters in anti-de Sitter spacetime. Magnetically charged black holes in an extended phase space are investigated. We obtain the mass and metric functions and the asymptotic and corrections to the Reissner–Nordström metric function [...] Read more.
We study Einstein’s gravity coupled to nonlinear electrodynamics with two parameters in anti-de Sitter spacetime. Magnetically charged black holes in an extended phase space are investigated. We obtain the mass and metric functions and the asymptotic and corrections to the Reissner–Nordström metric function when the cosmological constant vanishes. The first law of black hole thermodynamics in an extended phase space is formulated and the magnetic potential and the thermodynamic conjugate to the coupling are obtained. We prove the generalized Smarr relation. The heat capacity and the Gibbs free energy are computed and the phase transitions are studied. It is shown that the electric fields of charged objects at the origin and the electrostatic self-energy are finite within the nonlinear electrodynamics proposed. Full article
(This article belongs to the Special Issue Trends in the Second Law of Thermodynamics)
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27 pages, 3988 KiB  
Article
Methods to Calculate Entropy Generation
by Jude A. Osara and Michael D. Bryant
Entropy 2024, 26(3), 237; https://doi.org/10.3390/e26030237 - 7 Mar 2024
Cited by 2 | Viewed by 3327
Abstract
Entropy generation, formulated by combining the first and second laws of thermodynamics with an appropriate thermodynamic potential, emerges as the difference between a phenomenological entropy function and a reversible entropy function. The phenomenological entropy function is evaluated over an irreversible path through thermodynamic [...] Read more.
Entropy generation, formulated by combining the first and second laws of thermodynamics with an appropriate thermodynamic potential, emerges as the difference between a phenomenological entropy function and a reversible entropy function. The phenomenological entropy function is evaluated over an irreversible path through thermodynamic state space via real-time measurements of thermodynamic states. The reversible entropy function is calculated along an ideal reversible path through the same state space. Entropy generation models for various classes of systems—thermal, externally loaded, internally reactive, open and closed—are developed via selection of suitable thermodynamic potentials. Here we simplify thermodynamic principles to specify convenient and consistently accurate system governing equations and characterization models. The formulations introduce a new and universal Phenomenological Entropy Generation (PEG) theorem. The systems and methods presented—and demonstrated on frictional wear, grease degradation, battery charging and discharging, metal fatigue and pump flow—can be used for design, analysis, and support of diagnostic monitoring and optimization. Full article
(This article belongs to the Special Issue Trends in the Second Law of 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.

Tentative title: Thermodynamic modelling of the Ga-Nd binary system.
Authors: M. Ait Boukideura, H. Azzaa, M. Hammadib, H. Bouchtaa,c , M. Idbenalia,d, F.Z. Chrifi Alaouia, N. Selhaouia  and K. Mahdouka.

Affiliations:

a Laboratory of Thermodynamics and Energy (L. T. E.), Department of Physics, Faculty of Sciences, University Ibn Zohr, PO 8106, Hay Dakhla, 80000 Agadir, Morocco

b Laboratory for the Physico-Mechanical and Metallurgical Development and Characterization of Materials. Faculty of Exact Sciences and Computer Science - Mostaganem - Algeria

c Laboratory of Sustainable Innovation and Applied Research, International University of Agadir (Universiapolis), Agadir, Morocco.

d Centre Régional des Métiers de l’Education et de la Formation Inezgane, Académie Sous Massa, Agadir, Morocco.

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