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Special Issue "Entropy and the Second Law of 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 (20 December 2013)

Special Issue Editor

Guest Editor
Prof. Dr. Milivoje M. Kostic (Website1, Website2)

Department of Mechanical Engineering, Northern Illinois University, DeKalb, IL 60115, USA
Interests: fundamental laws of nature; thermodynamics and heat transfer fundamentals; the second law of thermodynamics and entropy; energy efficiency; conservation and sustainability; fluids-thermal-energy components and systems; nanotechnology and nanofluids

Special Issue Information

Dear Colleagues,

The goal of this special issue is to put certain physical and philosophical concepts in perspective, to revisit the fundamentals of the Second Law of Thermodynamics and concept of Entropy, as well as to initiate discussion and constructive criticism about these fundamental concepts, including some recent challenges of the Second Law.
The Second Law of Thermodynamics is among the most fundamental principles of engineering, science and nature. It provides conditions and limits for forced, directional displacement of mass-energy in space and time, thus governs all processes in nature. Since its discovery more than one-and-a-half century ago, its status is generally considered supreme.
Sadi Carnot’s ingenious reasoning of reversible processes and cycles (1824) laid foundations for The Second Law before The First Law of energy conservation was even known (Joule 1843) and long before Thermodynamic concepts were established in 1850s. A century later, Bridgman (1941) ‘complained’ that “there are almost as many formulations of The Second Law as there have been discussions of it.” Von Neumann once remarked that “whoever uses the term ‘entropy’ in a discussion always wins since no one knows what entropy really is, so in a debate one always has the advantage.” Einstein, whose early writings were related to the Second Law, remained convinced throughout his life that “Thermodynamics is the only universal physical theory that will never be refuted.”
There are many puzzling issues surrounding the Second Law and other concepts in Thermodynamics, including subtle definitions and ambiguous meaning of very fundamental concepts. Further confusions are produced by attempts to generalize some of those concepts with similar but not the same concepts in other disciplines, like Thermodynamic Entropy versus other types of entropies.
The Second Law is often challenged in biology, life and social sciences, including evolution and information sciences, all with history rich in confusion. Creation and organization of technical (man-made) and natural (including life) structures and thus ‘creation of local non-equilibrium’ is possible and is always happening in many processes while entropy is generated (never destroyed), using another functional structures (channeling, filtering, hardware/software templates, pumping, devices and tools, information knowledge-‘intelligent’ templates, DNAs, etc.). However, the mass-energy flow (transfer) within those structures will always and everywhere dissipate energy and generate entropy (according to the Second Law!), i.e. on the expense of internal and/or surrounding/boundary systems' non-equilibrium. It may appear that the created non-equilibrium structures are self-organizing from nowhere, from within an equilibrium (thus violating the Second Law), due to the lack of proper observations and ‘accounting’ of all mass-energy flows, the latter maybe in ‘stealth’ form or undetected rate at our state of technology and comprehension (as the science history has taught us many times).
The miracles are until we comprehend and explain them!
We welcome submissions addressing such fundamental issues as well as those on more specific topics illustrating the broad impact of the Second Law of Thermodynamics and the concepts of entropy (property) and entropy generation (as measure of process irreversibility).
Specific topics of interest include (but are not limited to):


• Carnot cycle and heat engine fundamentals and applications
• Reversibility and Irreversibility
• Thermodynamic temperature
• Entropy fundamentals and Clausius Equality and Inequality
• Non-equilibrium processes and ‘entropy generation’
• Work availability and Exergy
• Second Law of Thermodynamics – concept and fundamentals
• Equivalency of different Second Law statements
• Second Law and Statistical Thermodynamics
• Second Law and Quantum theory
• Perpetual motion of the second kind
• Maxwell’s Demon and other challenges


It is hoped that this special issue will inspire and motivate the scientists and practitioners to revisit important and critical issues related to the Second Law of Thermodynamics as one among the most if not the most relevant fundamental laws of nature.

Prof. M. Kostic
Guest Editor

Submission

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. Papers will be published continuously (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as 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 refereed through a 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 1400 CHF (Swiss Francs).

Published Papers (11 papers)

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Research

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Open AccessArticle On Spatial Covariance, Second Law of Thermodynamics and Configurational Forces in Continua
Entropy 2014, 16(6), 3234-3256; doi:10.3390/e16063234
Received: 27 December 2013 / Revised: 10 February 2014 / Accepted: 12 May 2014 / Published: 10 June 2014
Cited by 1 | PDF Full-text (457 KB) | HTML Full-text | XML Full-text
Abstract
This paper studies the transformation properties of the spatial balance of energy equation for a dissipative material, under the superposition of arbitrary spatial diffeomorphisms. The study reveals that for a dissipative material the transformed energy balance equation has some non-standard terms in [...] Read more.
This paper studies the transformation properties of the spatial balance of energy equation for a dissipative material, under the superposition of arbitrary spatial diffeomorphisms. The study reveals that for a dissipative material the transformed energy balance equation has some non-standard terms in it. These terms are related to a system of microforces with its own balance equation. These microforces act during the superposition of the spatial diffeomorphism, because of the dissipative properties of the material. Moreover, it is shown that for the case in question the stress tensor is additively decomposed into a conventional part given by the standard Doyle-Ericksen formula and a non-conventional one which is related to changes in the material internal structure in the course of deformation. On the basis of the second law of thermodynamics and the integrability condition of a Pfaffian form it is shown that the non-conventional part of the stress tensor can be related not only to dissipative but also to conservative response. A further insight to this conservative response is provided by exploiting the invariance properties of the balance of energy equation within the context of the material intrinsic “physical” metric concept. In this case, it is shown that the assumption of spatial covariance yields the standard conservation and balance laws of classical mechanics but it does not yield the standard Doyle-Ericksen formula. In fact, the Doyle-Ericksen formula has an additional term in it, which is related directly to the evolution of the material internal structure, as it is determined by the (time) evolution of the material metric in the spatial configuration. A formal connection between this term and the Eshelby energy-momentum tensor is derived as well. Full article
(This article belongs to the Special Issue Entropy and the Second Law of Thermodynamics)
Open AccessArticle Equivalent Temperature-Enthalpy Diagram for the Study of Ejector Refrigeration Systems
Entropy 2014, 16(5), 2669-2685; doi:10.3390/e16052669
Received: 13 January 2014 / Revised: 17 April 2014 / Accepted: 4 May 2014 / Published: 14 May 2014
Cited by 2 | PDF Full-text (463 KB) | HTML Full-text | XML Full-text
Abstract
The Carnot factor versus enthalpy variation (heat) diagram has been used extensively for the second law analysis of heat transfer processes. With enthalpy variation (heat) as the abscissa and the Carnot factor as the ordinate the area between the curves representing the [...] Read more.
The Carnot factor versus enthalpy variation (heat) diagram has been used extensively for the second law analysis of heat transfer processes. With enthalpy variation (heat) as the abscissa and the Carnot factor as the ordinate the area between the curves representing the heat exchanging media on this diagram illustrates the exergy losses due to the transfer. It is also possible to draw the paths of working fluids in steady-state, steady-flow thermodynamic cycles on this diagram using the definition of “the equivalent temperature” as the ratio between the variations of enthalpy and entropy in an analyzed process. Despite the usefulness of this approach two important shortcomings should be emphasized. First, the approach is not applicable for the processes of expansion and compression particularly for the isenthalpic processes taking place in expansion valves. Second, from the point of view of rigorous thermodynamics, the proposed ratio gives the temperature dimension for the isobaric processes only. The present paper proposes to overcome these shortcomings by replacing the actual processes of expansion and compression by combinations of two thermodynamic paths: isentropic and isobaric. As a result the actual (not ideal) refrigeration and power cycles can be presented on equivalent temperature versus enthalpy variation diagrams. All the exergy losses, taking place in different equipments like pumps, turbines, compressors, expansion valves, condensers and evaporators are then clearly visualized. Moreover the exergies consumed and produced in each component of these cycles are also presented. The latter give the opportunity to also analyze the exergy efficiencies of the components. The proposed diagram is finally applied for the second law analysis of an ejector based refrigeration system. Full article
(This article belongs to the Special Issue Entropy and the Second Law of Thermodynamics)
Open AccessArticle Entropy and Exergy Analysis of a Heat Recovery Vapor Generator for Ammonia-Water Mixtures
Entropy 2014, 16(4), 2056-2070; doi:10.3390/e16042056
Received: 6 January 2014 / Revised: 7 April 2014 / Accepted: 9 April 2014 / Published: 11 April 2014
Cited by 4 | PDF Full-text (314 KB) | HTML Full-text | XML Full-text
Abstract
Recently power generation systems using ammonia-water binary mixtures as a working fluid have been attracting much attention for their efficient conversion of low-grade heat sources into useful energy forms. This paper presents the First and Second Law thermodynamic analysis for a heat [...] Read more.
Recently power generation systems using ammonia-water binary mixtures as a working fluid have been attracting much attention for their efficient conversion of low-grade heat sources into useful energy forms. This paper presents the First and Second Law thermodynamic analysis for a heat recovery vapor generator (HRVG) of ammonia-water mixtures when the heat source is low-temperature energy in the form of sensible heat. In the analysis, key parameters such as ammonia mass concentration and pressure of the binary mixture are studied to investigate their effects on the system performance, including the effectiveness of heat transfer, entropy generation, and exergy efficiency. The results show that the ammonia concentration and the pressure of the mixture have significant effects on the system performance of the HRVG. Full article
(This article belongs to the Special Issue Entropy and the Second Law of Thermodynamics)
Open AccessArticle Entropy and Its Correlations with Other Related Quantities
Entropy 2014, 16(2), 1089-1100; doi:10.3390/e16021089
Received: 8 November 2013 / Revised: 21 January 2014 / Accepted: 27 January 2014 / Published: 19 February 2014
PDF Full-text (253 KB) | HTML Full-text | XML Full-text
Abstract
In order to find more correlations between entropy and other related quantities, an analogical analysis is conducted between thermal science and other branches of physics. Potential energy in various forms is the product of a conserved extensive quantity (for example, mass or [...] Read more.
In order to find more correlations between entropy and other related quantities, an analogical analysis is conducted between thermal science and other branches of physics. Potential energy in various forms is the product of a conserved extensive quantity (for example, mass or electric charge) and an intensive quantity which is its potential (for example, gravitational potential or electrical voltage), while energy in specific form is a dissipative quantity during irreversible transfer process (for example mechanical or electrical energy will be dissipated as thermal energy). However, it has been shown that heat or thermal energy, like mass or electric charge, is conserved during heat transfer processes. When a heat transfer process is for object heating or cooling, the potential of internal energy U is the temperature T and its potential “energy” is UT/2 (called entransy and it is the simplified expression of thermomass potential energy); when a heat transfer process is for heat-work conversion, the potential of internal energy U is (1 − T0/T), and the available potential energy of a system in reversible heat interaction with the environment is U U0 T0(S S0), then T0/T and T0(S S0) are the unavailable potential and the unavailable potential energy of a system respectively. Hence, entropy is related to the unavailable potential energy per unit environmental temperature for heat-work conversion during reversible heat interaction between the system and its environment. Entropy transfer, like other forms of potential energy transfer, is the product of the heat and its potential, the reciprocal of temperature, although it is in form of the quotient of the heat and the temperature. Thus, the physical essence of entropy transfer is the unavailable potential energy transfer per unit environmental temperature. Entropy is a non-conserved, extensive, state quantity of a system, and entropy generation in an irreversible heat transfer process is proportional to the destruction of available potential energy. Full article
(This article belongs to the Special Issue Entropy and the Second Law of Thermodynamics)
Open AccessArticle The Elusive Nature of Entropy and Its Physical Meaning
Entropy 2014, 16(2), 953-967; doi:10.3390/e16020953
Received: 2 January 2014 / Revised: 10 February 2014 / Accepted: 10 February 2014 / Published: 17 February 2014
Cited by 3 | PDF Full-text (320 KB) | HTML Full-text | XML Full-text
Abstract
Entropy is the most used and often abused concept in science, but also in philosophy and society. Further confusions are produced by some attempts to generalize entropy with similar but not the same concepts in other disciplines. The physical meaning of phenomenological, [...] Read more.
Entropy is the most used and often abused concept in science, but also in philosophy and society. Further confusions are produced by some attempts to generalize entropy with similar but not the same concepts in other disciplines. The physical meaning of phenomenological, thermodynamic entropy is reasoned and elaborated by generalizing Clausius definition with inclusion of generated heat, since it is irrelevant if entropy is changed due to reversible heat transfer or irreversible heat generation. Irreversible, caloric heat transfer is introduced as complementing reversible heat transfer. It is also reasoned and thus proven why entropy cannot be destroyed but is always generated (and thus over-all increased) locally and globally, at every space and time scales, without any exception. It is concluded that entropy is a thermal displacement (dynamic thermal-volume) of thermal energy due to absolute temperature as a thermal potential (dQ = TdS), and thus associated with thermal heat and absolute temperature, i.e., distribution of thermal energy within thermal micro-particles in space. Entropy is an integral measure of (random) thermal energy redistribution (due to heat transfer and/or irreversible heat generation) within a material system structure in space, per absolute temperature level: dS = dQSys/T = mCSysdT/T, thus logarithmic integral function, with J/K unit. It may be also expressed as a measure of “thermal disorder”, being related to logarithm of number of all thermal, dynamic microstates W (their position and momenta), S = kBlnW, or to the sum of their logarithmic probabilities S = −kB∑pilnpi, that correspond to, or are consistent with the given thermodynamic macro-state. The number of thermal microstates W, is correlated with macro-properties temperature T and volume V for ideal gases. A system form and/or functional order or disorder are not (thermal) energy order/disorder and the former is not related to Thermodynamic entropy. Expanding entropy to any type of disorder or information is a source of many misconceptions. Granted, there are certain benefits of simplified statistical descriptions to better comprehend the randomness of thermal motion and related physical quantities, but the limitations should be stated so the generalizations are not overstretched and the real physics overlooked, or worse discredited. Full article
(This article belongs to the Special Issue Entropy and the Second Law of Thermodynamics)
Open AccessArticle Reducing Entropy Generation in MHD Fluid Flow over Open Parallel Microchannels Embedded in a Micropatterned Permeable Surface
Entropy 2013, 15(11), 4822-4843; doi:10.3390/e15114822
Received: 26 July 2013 / Revised: 7 October 2013 / Accepted: 21 October 2013 / Published: 6 November 2013
Cited by 8 | PDF Full-text (390 KB) | HTML Full-text | XML Full-text
Abstract
The present study examines embedded open parallel microchannels within a micropatterned permeable surface for reducing entropy generation in MHD fluid flow in microscale systems. A local similarity solution for the transformed governing equations is obtained. The governing partial differential equations along with [...] Read more.
The present study examines embedded open parallel microchannels within a micropatterned permeable surface for reducing entropy generation in MHD fluid flow in microscale systems. A local similarity solution for the transformed governing equations is obtained. The governing partial differential equations along with the boundary conditions are first cast into a dimensionless form and then the reduced ordinary differential equations are solved numerically via the Dormand-Prince pair and shooting method. The dimensionless entropy generation number is formulated by an integral of the local rate of entropy generation along the width of the surface based on an equal number of microchannels and no-slip gaps interspersed between those microchannels. Finally, the entropy generation numbers, as well as the Bejan number, are investigated. It is seen that surface-embedded microchannels can successfully reduce entropy generation in the presence of an applied magnetic field. Full article
(This article belongs to the Special Issue Entropy and the Second Law of Thermodynamics)
Open AccessArticle Entropy Generation in a Couple Stress Fluid Flow Through a Vertical Channel Filled with Saturated Porous Media
Entropy 2013, 15(11), 4589-4606; doi:10.3390/e15114589
Received: 16 September 2013 / Revised: 6 October 2013 / Accepted: 21 October 2013 / Published: 25 October 2013
Cited by 13 | PDF Full-text (336 KB) | HTML Full-text | XML Full-text
Abstract
The present work investigates numerically the inherent irreversibility in a steady flow of a couple stress fluid through a vertical channel packed with saturated porous substances. The First and Second Laws of Thermodynamics are applied to analyze the problem. The nonlinear governing [...] Read more.
The present work investigates numerically the inherent irreversibility in a steady flow of a couple stress fluid through a vertical channel packed with saturated porous substances. The First and Second Laws of Thermodynamics are applied to analyze the problem. The nonlinear governing equations in Cartesian coordinates are obtained and solved numerically using shooting methods together with a Runge-Kutta Fehlberg integration scheme. The entropy generation number is computed by utilizing the velocity and temperature profiles. The effects of various physical parameters on the flow and heat transfer characteristics, as well as entropy generation rates and Bejan number, are investigated through graphs. Full article
(This article belongs to the Special Issue Entropy and the Second Law of Thermodynamics)
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Open AccessArticle Energy, Entropy and Exergy in Communication Networks
Entropy 2013, 15(10), 4484-4503; doi:10.3390/e15104484
Received: 3 June 2013 / Revised: 2 October 2013 / Accepted: 11 October 2013 / Published: 18 October 2013
Cited by 7 | PDF Full-text (1508 KB) | HTML Full-text | XML Full-text
Abstract
The information and communication technology (ICT) sector is continuously growing, mainly due to the fast penetration of ICT into many areas of business and society. Growth is particularly high in the area of technologies and applications for communication networks, which can be [...] Read more.
The information and communication technology (ICT) sector is continuously growing, mainly due to the fast penetration of ICT into many areas of business and society. Growth is particularly high in the area of technologies and applications for communication networks, which can be used, among others, to optimize systems and processes. The ubiquitous application of ICT opens new perspectives and emphasizes the importance of understanding the complex interactions between ICT and other sectors. Complex and interacting heterogeneous systems can only properly be addressed by a holistic framework. Thermodynamic theory, and, in particular, the second law of thermodynamics, is a universally applicable tool to analyze flows of energy. Communication systems and their processes can be seen, similar to many other natural processes and systems, as dissipative transformations that level differences in energy density between participating subsystems and their surroundings. This paper shows how to apply thermodynamics to analyze energy flows through communication networks. Application of the second law of thermodynamics in the context of the Carnot heat engine is emphasized. The use of exergy-based lifecycle analysis to assess the sustainability of ICT systems is shown on an example of a radio access network. Full article
(This article belongs to the Special Issue Entropy and the Second Law of Thermodynamics)
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Open AccessArticle Gravitational Entropy and Inflation
Entropy 2013, 15(9), 3620-3639; doi:10.3390/e15093620
Received: 28 June 2013 / Revised: 16 July 2013 / Accepted: 30 August 2013 / Published: 4 September 2013
PDF Full-text (427 KB) | HTML Full-text | XML Full-text
Abstract
The main topic of this paper is a description of the generation of entropy at the end of the inflationary era. As a generalization of the present standard model of the Universe dominated by pressureless dust and a Lorentz invariant vacuum energy [...] Read more.
The main topic of this paper is a description of the generation of entropy at the end of the inflationary era. As a generalization of the present standard model of the Universe dominated by pressureless dust and a Lorentz invariant vacuum energy (LIVE), we first present a flat Friedmann universe model, where the dust is replaced with an ideal gas. It is shown that the pressure of the gas is inversely proportional to the fifth power of the scale factor and that the entropy in a comoving volume does not change during the expansion. We then review different measures of gravitational entropy related to the Weyl curvature conjecture and calculate the time evolution of two proposed measures of gravitational entropy in a LIVE-dominated Bianchi type I universe, and a Lemaitre-Bondi-Tolman universe with LIVE. Finally, we elaborate upon a model of energy transition from vacuum energy to radiation energy, that of Bonanno and Reuter, and calculate the time evolution of the entropies of vacuum energy and radiation energy. We also calculate the evolution of the maximal entropy according to some recipes and demonstrate how a gap between the maximal entropy and the actual entropy opens up at the end of the inflationary era. Full article
(This article belongs to the Special Issue Entropy and the Second Law of Thermodynamics)
Open AccessArticle General Formula for the Efficiency of Quantum-Mechanical Analog of the Carnot Engine
Entropy 2013, 15(4), 1408-1415; doi:10.3390/e15041408
Received: 24 January 2013 / Revised: 9 April 2013 / Accepted: 11 April 2013 / Published: 17 April 2013
Cited by 6 | PDF Full-text (179 KB) | HTML Full-text | XML Full-text
Abstract
An analog of the Carnot engine reversibly operating within the framework of pure-state quantum mechanics is discussed. A general formula is derived for the efficiency of such an engine with an arbitrary confining potential. Its expression is given in terms of an [...] Read more.
An analog of the Carnot engine reversibly operating within the framework of pure-state quantum mechanics is discussed. A general formula is derived for the efficiency of such an engine with an arbitrary confining potential. Its expression is given in terms of an energy spectrum and shows how the efficiency depends on a potential as the analog of a working material in thermodynamics, in general. This non-universal nature results from the fact that there exists no analog of the second law of thermodynamics in pure-state quantum mechanics where the von Neumann entropy identically vanishes. A special class of spectra, which leads to a common form of the efficiency, is identified. Full article
(This article belongs to the Special Issue Entropy and the Second Law of Thermodynamics)

Review

Jump to: Research

Open AccessReview On the Entropy of a Class of Irreversible Processes
Entropy 2013, 15(8), 2975-2988; doi:10.3390/e15082975
Received: 19 April 2013 / Revised: 5 June 2013 / Accepted: 9 July 2013 / Published: 26 July 2013
Cited by 2 | PDF Full-text (242 KB) | HTML Full-text | XML Full-text
Abstract
We review a recent technique for determining the entropy change accompanying certain classes of irreversible processes involving changes in the state of a system anchored to a reservoir. Time is introduced as a parameter to specify the corresponding entropy evolution of the [...] Read more.
We review a recent technique for determining the entropy change accompanying certain classes of irreversible processes involving changes in the state of a system anchored to a reservoir. Time is introduced as a parameter to specify the corresponding entropy evolution of the system. The procedural details are outlined and their relation to the standard treatment of irreversible processes is examined. Full article
(This article belongs to the Special Issue Entropy and the Second Law of Thermodynamics)

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